2024/2025
Authors: Daniel Gutierrez & Fabio Pimentel
# Required Packages--------------------
rm(list = ls())
library(readxl)
library(ggplot2)
library(GGally)
Registered S3 method overwritten by 'GGally':
method from
+.gg ggplot2
library(dplyr)
Attaching package: ‘dplyr’
The following objects are masked from ‘package:stats’:
filter, lag
The following objects are masked from ‘package:base’:
intersect, setdiff, setequal, union
library(lubridate)
Attaching package: ‘lubridate’
The following objects are masked from ‘package:base’:
date, intersect, setdiff, union
library(corrplot)
corrplot 0.95 loaded
library(feasts)
Loading required package: fabletools
Registered S3 method overwritten by 'tsibble':
method from
as_tibble.grouped_df dplyr
library(tsibble)
Attaching package: ‘tsibble’
The following object is masked from ‘package:lubridate’:
interval
The following object is masked from ‘package:zoo’:
index
The following objects are masked from ‘package:base’:
intersect, setdiff, union
library(forecast)
library(tidyr)
Attaching package: ‘tidyr’
The following object is masked from ‘package:reshape2’:
smiths
library(ggthemes)
library(car)
Loading required package: carData
Attaching package: ‘car’
The following object is masked from ‘package:dplyr’:
recode
library(DIMORA)
library(tseries)
‘tseries’ version: 0.10-58
‘tseries’ is a package for time series analysis and computational finance.
See ‘library(help="tseries")’ for details.
library(lmtest)
#setwd('/Users/fabiopimentel/Documents/Padua/clases/segundo año primer semestre/BEF data/proyecto/time_series_padova-main')
# target variable
sales <- read_excel("data/sales/sales_dimsum_31102024.xlsx")
sales[is.na(sales)] <- 0 # set to zero na values
#setwd('/Users/fabiopimentel/Documents/Padua/clases/segundo año primer semestre/BEF data/proyecto/time_series_padova-main')
# target variable
sales <- read_excel("data/sales/sales_dimsum_31102024.xlsx")
sales[is.na(sales)] <- 0 # set to zero na values
# economic variables
eco_growth <- read_excel("data/macroeconomic/economic_activity.xlsx")
fx <- read_excel("data/macroeconomic/fx.xlsx") #Foreign exchange is the conversion of one currency into another
inflation <- read_excel("data/macroeconomic/inflation.xlsx")
unemployment <- read_excel("data/macroeconomic/unemployment.xlsx")
str(sales)
str(eco_growth)
```r
# other variables
google_trends <- read_excel(\data/other/google_trends_restaurantes.xlsx\)
rain <- read_excel(\data/other/rain_proxy.xlsx\)
temp <- read_excel(\data/other/temperature_data.xlsx\)
temp[is.na(temp)] <- 0
rain[is.na(rain)] <- 0
plot(temp$tavg) # no zeros in temp : OK
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```r
str(inflation)
str(unemployment)
str(google_trends)
str(rain)
str(temp) # this has NaNs, must fill somehow
# sales
## sales monthly
df_sales_m <- sales %>%
mutate(month = floor_date(date, "month")) %>% # Extract month
group_by(month) %>%
summarise(sales_m = sum(sales_cop), bar_m = sum(bar), food_m = sum(food)
) # Summing values
head(df_sales_m)
# sales
## sales monthly
df_sales_m <- sales %>%
mutate(month = floor_date(date, "month")) %>% # Extract month
group_by(month) %>%
summarise(sales_m = sum(sales_cop), bar_m = sum(bar), food_m = sum(food)
) # Summing values
head(df_sales_m)
## sales weekly
df_sales_w <- sales %>%
mutate(week = floor_date(date, "week")) %>% # Extract month
group_by(week) %>%
summarise(sales_w = sum(sales_cop), bar_w = sum(bar), food_w = sum(food)) # Summing values
head(df_sales_w)
# fx
df_fx_m <- fx %>%
mutate(month = floor_date(date, "month")) %>%
group_by(month) %>%
summarise(fx_m = mean(fx))
df_fx_w <- fx %>%
mutate(week = floor_date(date, "week")) %>%
group_by(week) %>%
summarise(fx_w = mean(fx))
head(df_fx_m)
head(df_fx_w)
# google trends
# montly
df_google_m <- google_trends %>%
mutate(month = floor_date(date, "month")) %>%
group_by(month) %>%
summarise(google_m = mean(google_trends))
# weekly
df_google_w <- google_trends %>%
mutate(week = floor_date(date, "week")) %>%
group_by(week) %>%
summarise(google_w = mean(google_trends))
head(df_google_m)
head(df_google_w)
## rain
df_rain_g = rain %>%
group_by(date, region) %>%
summarise(rain_sum=sum(contribution_m3s))
`summarise()` has grouped output by 'date'. You can override using the `.groups` argument.
df_rain_g <- df_rain_g[df_rain_g$region=="ANTIOQUIA",]
head(df_rain_g)
# montly
df_rain_m <- df_rain_g %>%
mutate(month = floor_date(date, "month")) %>%
group_by(month) %>%
summarise(rain_m = sum(rain_sum))
# weekly
df_rain_w <- df_rain_g %>%
mutate(week = floor_date(date, "week")) %>%
group_by(week) %>%
summarise(rain_w = sum(rain_sum))
head(df_rain_m)
head(df_rain_w)
objects_to_keep <- c("df_merged_d", "df_merged_w", "df_merged_m")
# Remove all objects except those specified
rm(list = setdiff(ls(), objects_to_keep))
We want to move to a stacked bar chart when we care about the relative decomposition of each primary bar based on the levels of a second categorical variable. Each bar is now comprised of a number of sub-bars, each one corresponding with a level of a secondary categorical variable. The total length of each stacked bar is the same as before, but now we can see how the secondary groups contributed to that total.
One important consideration in building a stacked bar chart is to decide which of the two categorical variables will be the primary variable (dictating major axis positions and overall bar lengths) and which will be the secondary (dictating how each primary bar will be subdivided). The most ‘important’ variable should be the primary; use domain knowledge and the specific type of categorical variables to make a decision on how to assign your categorical variables
#Monthly
# Reshape the data to a long format
df_sales_m_long <- df_merged_m %>%
pivot_longer(cols = c(bar_m, food_m), names_to = "Category", values_to = "Value")
# Create the stacked bar plot
ggplot(df_sales_m_long, aes(x = month, y = Value, fill = Category)) +
geom_bar(stat = "identity", position = "stack") +
ggtitle("Monthly Sales of Restaurant") +
labs(y = "Sales", x = "Month", fill = "Category") +
theme_minimal()
df_sales_w_long <- df_merged_w %>%
pivot_longer(cols = c(bar_w, food_w), names_to = "Category", values_to = "Value")
# Create the stacked bar plot
ggplot(df_sales_w_long, aes(x = week, y = Value, fill = Category)) +
geom_bar(stat = "identity", position = "stack") +
ggtitle("Weekly Sales of Restaurant") +
labs(y = "Sales", x = "Week", fill = "Category") +
theme_minimal()
# Seasonal plots
df_sales_w_filtered <- df_merged_w %>%
filter(week >= ymd("2021-12-31"))
tseries_w <- ts(df_sales_w_filtered$sales_w , start = c(2022, 1), frequency = 52)
head(tseries_w)
Time Series:
Start = c(2022, 1)
End = c(2022, 6)
Frequency = 52
[1] 5654618 5894371 8308052 9164178 11934123
[6] 9777570
seasonplot(tseries_w, col = rainbow(3), year.labels = TRUE, main = "Seasonal Plot")
text(x = 1, y = max(tseries_w) - 1.5e7, labels = "2024", col = "blue")
NA
NA
# seasonplot monthly
df_sales_m_filtered <- df_merged_m %>%
filter(month >= ymd("2021-12-31"))
tseries_m <- ts(df_sales_m_filtered$sales_m , start = c(2022, 1), frequency = 12)
head(tseries_m)
Jan Feb Mar Apr
2022 31953282 41926179 37466677 57926246
May Jun
2022 79622843 88816435
seasonplot(tseries_m, col = rainbow(3), year.labels = TRUE, main = "Seasonal Plot")
text(x = 1, y = max(tseries_m) - 1e6, labels = "2024", col = "blue")
# Montly Density
# Select the columns of interest
variables <- c("sales_m", "bar_m", "food_m", "rain_m", "fx_m", "google_m",
"ise", "inflation", "unemployment", "temp_m", "prcp_m")
# Transform the data to long format for ggplot2
df_long_m <- df_merged_m %>%
pivot_longer(cols = all_of(variables), names_to = "Variable", values_to = "Value")
# Create the grid of density plots
ggplot(df_long_m, aes(x = Value)) +
geom_density(fill = "blue", alpha = 0.4) +
facet_wrap(~ Variable, scales = "free", ncol = 3) +
labs(title = "Density Plots of Selected Variables",
x = "Value", y = "Density") +
theme_minimal()
# Weekly Density
# Select the columns of interest
variables <- c("sales_w", "bar_w", "food_w", "rain_w", "fx_w", "google_w",
"temp_w", "prcp_w")
df_long_w <- df_merged_w %>%
pivot_longer(cols = all_of(variables), names_to = "Variable", values_to = "Value")
# Create the grid of density plots
ggplot(df_long_w, aes(x = Value)) +
geom_density(fill = "blue", alpha = 0.4) +
facet_wrap(~ Variable, scales = "free", ncol = 3) +
labs(title = "Density Plots of Selected Variables",
x = "Value", y = "Density") +
theme_minimal()
# Daily Density
# Select the columns of interest
variables <- c("sales_cop", "bar", "food", "rain_sum", "fx",
"tmedian", "prcp")
df_long_d <- df_merged_d %>%
pivot_longer(cols = all_of(variables), names_to = "Variable", values_to = "Value")
# Create the grid of density plots
ggplot(df_long_d, aes(x = Value)) +
geom_density(fill = "blue", alpha = 0.4) +
facet_wrap(~ Variable, scales = "free", ncol = 3) +
labs(title = "Density Plots of Selected Variables",
x = "Value", y = "Density") +
theme_minimal()
### 3.5.1 economic variables-----------------------
# economic growth
ggplot(df_merged_m, aes(x=month, y=ise)) +
geom_line() + ggtitle("Monthly activity in Colombia")
# clearly seasonal and trend
# fx
ggplot(df_merged_d, aes(x=date, y=fx)) +
geom_line() + ggtitle("Daily COP/USD")
# trend but no clear seasonality
# inflation
ggplot(df_merged_m, aes(x=month, y=inflation)) +
geom_line() + ggtitle("Monthly inflation National")
# business cycles, no tend or seasonality
# unemployment
ggplot(df_merged_m, aes(x=month, y=unemployment)) +
geom_line() + ggtitle("Montly trailing unemployment Medellin")
# seasonal and trend downwards
### 3.5.2 Other variables
# google trends
ggplot(df_merged_w, aes(x=week, y=google_w)) +
geom_line() + ggtitle("Weelkly Google trends 'Restaurantes'")
# no clear behaviour, drop in pandemic
# rain
ggplot(df_merged_d, aes(x=date, y=rain_sum)) +
geom_line() + ggtitle("Daily rain approximated in Antioquia")
# no trend or seasonality clearly
# temperature
ggplot(df_merged_d, aes(x=date, y=tmedian)) +
geom_line() + ggtitle("Daily Median temperature in Medellin")
# almost stationary
# temperature
ggplot(df_merged_d, aes(x=date, y=tavg)) +
geom_line() + ggtitle("Daily Average temperature in Medellin")
# this one looks weird, better keep working on median
# precipitation from temp
ggplot(df_merged_d, aes(x=date, y=prcp)) +
geom_line() + ggtitle("Daily precipitation in Medellin")
# looks decent
df_merged_d <- subset(df_merged_d, select = -region)
# daily
ggpairs(df_merged_d,
columns = 2:8)
# sales have correl with fx and rain_sum
# weekly
ggpairs(df_merged_w,
columns = 2:9)
# sales have correl with rain, google, fx, temp
# bar has more correl with temp
# montly
ggpairs(df_merged_m,
columns = 2:12)
# Exclude 'date' column
numeric_df_d <- df_merged_d[, sapply(df_merged_d, is.numeric)]
cor_matrix_d <- cor(numeric_df_d, use = "complete.obs") # Use only complete rows
cor_matrix_d
sales_cop bar food
sales_cop 1.000000000 0.895118281 0.98135791
bar 0.895118281 1.000000000 0.79301917
food 0.981357913 0.793019172 1.00000000
rain_sum 0.166252448 0.127567019 0.17164822
fx 0.146774104 0.136714885 0.14261504
tavg 0.008884659 0.089640797 -0.02562481
prcp 0.028085504 -0.001337552 0.03913167
tmedian 0.108891610 0.111686146 0.10120437
rain_sum fx tavg
sales_cop 0.1662524 0.14677410 0.008884659
bar 0.1275670 0.13671488 0.089640797
food 0.1716482 0.14261504 -0.025624811
rain_sum 1.0000000 0.63500919 -0.134005147
fx 0.6350092 1.00000000 0.164550220
tavg -0.1340051 0.16455022 1.000000000
prcp 0.1857676 0.05556529 -0.267367632
tmedian -0.2717930 -0.07710937 0.656170981
prcp tmedian
sales_cop 0.028085504 0.10889161
bar -0.001337552 0.11168615
food 0.039131672 0.10120437
rain_sum 0.185767588 -0.27179302
fx 0.055565287 -0.07710937
tavg -0.267367632 0.65617098
prcp 1.000000000 -0.22103872
tmedian -0.221038724 1.00000000
numeric_df_w <- df_merged_w[, sapply(df_merged_w, is.numeric)]
cor_matrix_w <- cor(numeric_df_w, use = "complete.obs") # Use only complete rows
cor_matrix_w
sales_w bar_w food_w
sales_w 1.00000000 0.8910033 0.98922211
bar_w 0.89100331 1.0000000 0.81506933
food_w 0.98922211 0.8150693 1.00000000
rain_w 0.29131607 0.2875652 0.27858415
google_w -0.44467552 -0.3551772 -0.45333238
fx_w 0.24395629 0.2873958 0.22038752
temp_w -0.02746535 0.1275798 -0.07507291
prcp_w 0.17241188 0.1211778 0.18095801
rain_w google_w fx_w
sales_w 0.2913161 -0.444675519 0.243956293
bar_w 0.2875652 -0.355177208 0.287395824
food_w 0.2785842 -0.453332380 0.220387520
rain_w 1.0000000 -0.107348280 0.662664730
google_w -0.1073483 1.000000000 -0.002777267
fx_w 0.6626647 -0.002777267 1.000000000
temp_w -0.1062959 0.208497604 0.193152564
prcp_w 0.3289820 -0.251630474 0.107858510
temp_w prcp_w
sales_w -0.02746535 0.1724119
bar_w 0.12757976 0.1211778
food_w -0.07507291 0.1809580
rain_w -0.10629590 0.3289820
google_w 0.20849760 -0.2516305
fx_w 0.19315256 0.1078585
temp_w 1.00000000 -0.3047876
prcp_w -0.30478758 1.0000000
numeric_df_m <- df_merged_m[, sapply(df_merged_m, is.numeric)]
cor_matrix_m <- cor(numeric_df_m, use = "complete.obs") # Use only complete rows
cor_matrix_m
sales_m bar_m food_m
sales_m 1.00000000 0.91772972 0.9930535
bar_m 0.91772972 1.00000000 0.8646613
food_m 0.99305351 0.86466133 1.0000000
rain_m 0.34590142 0.35781875 0.3316856
fx_m 0.26008119 0.33043881 0.2325461
google_m -0.60141163 -0.43583265 -0.6306910
ise 0.14184921 0.09197376 0.1528346
inflation 0.24620155 0.41865460 0.1885633
unemployment -0.47774546 -0.35355440 -0.4999277
temp_m -0.05360312 0.12366320 -0.1041492
prcp_m 0.28057040 0.20114717 0.2956418
rain_m fx_m
sales_m 0.345901419 0.260081195
bar_m 0.357818748 0.330438807
food_m 0.331685570 0.232546131
rain_m 1.000000000 0.700900212
fx_m 0.700900212 1.000000000
google_m -0.127328581 -0.016302700
ise 0.143925313 0.006203153
inflation 0.554477494 0.731585721
unemployment -0.314673431 -0.148857922
temp_m -0.004770513 0.242855832
prcp_m 0.364914544 0.106392263
google_m ise inflation
sales_m -0.60141163 0.141849210 0.2462015
bar_m -0.43583265 0.091973761 0.4186546
food_m -0.63069104 0.152834568 0.1885633
rain_m -0.12732858 0.143925313 0.5544775
fx_m -0.01630270 0.006203153 0.7315857
google_m 1.00000000 0.093304022 0.1600715
ise 0.09330402 1.000000000 -0.1118127
inflation 0.16007149 -0.111812691 1.0000000
unemployment 0.42550422 -0.602525241 -0.1308017
temp_m 0.33976804 -0.190530186 0.5982503
prcp_m -0.37823361 0.047259121 0.0657641
unemployment temp_m
sales_m -0.477745462 -0.053603118
bar_m -0.353554400 0.123663200
food_m -0.499927664 -0.104149167
rain_m -0.314673431 -0.004770513
fx_m -0.148857922 0.242855832
google_m 0.425504221 0.339768042
ise -0.602525241 -0.190530186
inflation -0.130801728 0.598250278
unemployment 1.000000000 -0.007286939
temp_m -0.007286939 1.000000000
prcp_m -0.415992203 -0.280144464
prcp_m
sales_m 0.28057040
bar_m 0.20114717
food_m 0.29564181
rain_m 0.36491454
fx_m 0.10639226
google_m -0.37823361
ise 0.04725912
inflation 0.06576410
unemployment -0.41599220
temp_m -0.28014446
prcp_m 1.00000000
# Plot the Correlation Matrix
par(mfrow=c(1,1))
corrplot(cor_matrix_d, method = "color", type = "upper", tl.col = "black", tl.srt = 45)
corrplot(cor_matrix_w, method = "color", type = "upper", tl.col = "black", tl.srt = 45)
corrplot(cor_matrix_m, method = "color", type = "upper", tl.col = "black", tl.srt = 45)
Rain has stronger correlation than prcp, so we drop prcp to not repeat the same variable from two sources Also we drop average temperature because median temperature seems more trustworthy
# drop prcp beacuse they "are the same"
df_merged_m <- df_merged_m %>% select(-prcp_m)
df_merged_w <- df_merged_w %>% select(-prcp_w)
df_merged_d <- df_merged_d %>% select(-prcp)
# drop avg temp
df_merged_d <- df_merged_d %>% select(-tavg)
colnames(df_merged_d)
[1] "date" "sales_cop" "bar"
[4] "food" "rain_sum" "fx"
[7] "tmedian"
### drop everything not on use
objects_to_keep <- c("df_merged_d", "df_merged_w", "df_merged_m")
# Remove all objects except those specified
rm(list = setdiff(ls(), objects_to_keep))
POSIXct and POSIXlt Classes
Times and date-times are represented by the POSIXct or the POSIXlt class in R. The POSIXct format stores date and time in seconds with the number of seconds beginning at January 1, 1970, so a POSIXct date-time is essentially an single value on a timeline. Date-times prior to 1970, will be negative numbers. The POSIXlt class stores other date and time information in a list such as hour of day of week, month of year, etc. The starting year for POSIXlt data is 1900, so 2022 would be stored as year 122. Months also begin at 0, so January is stored as month 0 and February as month 1. For both POSIX classes, the timezone can be classified. While date-times stored as POSIXct and POSIXlt look similar, when you unclass them with the unclass() function, you can see the additional information stored within the POSIXlt data.
Date Class
Dates without time can simply be stored as a Date class in R using the as.Date() function. Both Dates and POXIC classes need to be defined based on how they formatted. When uploading time series data into R, date and date-time data is typically uploaded as a character class and must be converted to date or time class using the as.Date(), as.POSIXct() or as.POSIXlt() functions.
Monthly
# Vars for model
# Month
# Ensure the `month` column is in POSIXct format
df_merged_m$month <- as.POSIXct(df_merged_m$month)
# Create the numeric variable: an evenly increasing number
df_merged_m <- df_merged_m %>%
arrange(month) %>% # Ensure data is sorted by month
mutate(numeric_month = row_number()) # Assign an increasing number
# Create the seasonal variable: the 12 different months as a factor
df_merged_m <- df_merged_m %>%
mutate(seasonal_month = factor(format(month, "%B"), levels = month.name)) # Month names as ordered factors
Weekly
# Week
# Ensure the `week` column is in POSIXct format
df_merged_w$week <- as.POSIXct(df_merged_w$week)
# Create the numeric variable: an evenly increasing number
df_merged_w <- df_merged_w %>%
arrange(week) %>% # Ensure data is sorted by week
mutate(numeric_week = row_number()) # Assign an increasing number
# Create the seasonal variable: the 12 different months as a factor
df_merged_w <- df_merged_w %>%
mutate(seasonal_month = factor(format(week, "%B"), levels = month.name)) # Month names as ordered factors
Daily
# Day
# Ensure the `day` column is in POSIXct format
df_merged_d$date <- as.POSIXct(df_merged_d$date)
# Create the numeric variable: an evenly increasing number
df_merged_d <- df_merged_d %>%
arrange(date) %>% # Ensure data is sorted by day
mutate(numeric_day = row_number()) # Assign an increasing number
# Create the seasonal variable: the 12 different months as a factor
df_merged_d <- df_merged_d %>%
mutate(seasonal_month = factor(format(date, "%B"), levels = month.name)) # Month names as ordered factors
# Create a column indicating the day of the week
df_merged_d <- df_merged_d %>%
mutate(day_of_week = factor(weekdays(date), levels = c("Monday", "Tuesday", "Wednesday",
"Thursday", "Friday", "Saturday", "Sunday"))) # Day of the week as ordered factor
Convert sales to time series objects for the use in several models
# convert to time series
sales_d_ts <- ts(df_merged_d$sales_cop)
sales_w_ts <- ts(df_merged_w$sales_w)
sales_m_ts <- ts(df_merged_m$sales_m)
par(mfrow=c(1,1))
# Daily
tsdisplay(sales_d_ts)
# is not stationary but has no clear trend
# and seasonality every 7 days
# Weekly
tsdisplay(sales_w_ts)
# not stationary: has trend
# Montly
tsdisplay(sales_m_ts)
# has clear trend, no seasonality
Some variables are scaled to log, so we can interpret the linear models more easily. The covariates are in different scales so it is easier to interpret percentage changes instead of unit changes.
# Monthly
df_merged_m <- df_merged_m %>%
mutate(across(where(is.numeric) & !all_of(c("unemployment", "inflation")), ~ log(. + 1)))
# Weekly
df_merged_w <- df_merged_w %>%
mutate(across(where(is.numeric), ~ log(. + 1)))
# Daily
# Weekly
df_merged_d <- df_merged_d %>%
mutate(across(where(is.numeric), ~ log(. + 1)))
#par(mfrow=c(1,1))
#tsdisplay(sales_d_ts)
# is not stationary but has no clear trend
plot(sales_d_ts)
acf(sales_d_ts)
pacf(sales_d_ts)
When data are seasonal, the autocorrelation will be larger for the seasonal lags (at multiples of the seasonal period) than for other lags.
# Weekly
#tsdisplay(sales_w_ts)
plot(sales_w_ts)
acf(sales_w_ts)
pacf(sales_w_ts)
# not stationary: has trend and seasonality maybe
# Montly
#tsdisplay(sales_m_ts)
plot(sales_m_ts)
acf(sales_m_ts)
pacf(sales_m_ts)
# has clear trend, no seasonality
In this section we model the time series using various approaches to find the best model for our data. We use both linear and non linear models going from the simplest to the more “complex” models.
Functions that help us implement and analyze models faster
## Function to create and summarize models------------------
run_model <- function(formula, data, model_name) {
cat("\nRunning", model_name, "\n")
model <- lm(formula, data = data)
print(summary(model))
par(mfrow = c(2, 2))
plot(model)
return(model)
}
# Function to compare models using ANOVA
compare_models <- function(model1, model2, name1, name2) {
cat("\nComparing Models:", name1, "vs", name2, "\n")
anova_result <- anova(model1, model2)
print(anova_result)
return(anova_result)
}
# Function to add predictions to the dataset
add_predictions <- function(model, data, pred_column) {
data[[pred_column]] <- predict(model, newdata = data)
return(data)
}
# Calculate RMSE
# Function to calculate RMSE
calculate_rmse <- function(observed, predicted) {
rmse <- sqrt(mean((observed - predicted)^2, na.rm = TRUE))
return(rmse)
}
# function that compares linear models
# Define the function to get R^2 and AIC
get_model_stats <- function(models) {
# Initialize an empty data frame
stats <- data.frame(
Model = character(),
R2 = numeric(),
AIC = numeric(),
stringsAsFactors = FALSE
)
# Loop through the list of models
for (i in seq_along(models)) {
model <- models[[i]]
model_name <- names(models)[i]
# Extract R^2 and AIC
r2 <- summary(model)$r.squared
aic <- AIC(model)
# Append to the data frame
stats <- rbind(stats, data.frame(Model = model_name, R2 = r2, AIC = aic))
}
return(stats)
}
# Montly Models
# View Dataframe
head(df_merged_m)
# Model 0: Trend only
ols0 <- run_model(sales_m ~ numeric_month, df_merged_m, "Model 0")
Running Model 0
Call:
lm(formula = formula, data = data)
Residuals:
Min 1Q Median 3Q Max
-0.9910 -0.1192 0.0158 0.1476 0.4953
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 16.40311 0.18031 90.97 < 2e-16 ***
numeric_month 0.68309 0.06312 10.82 1.49e-12 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.28 on 34 degrees of freedom
Multiple R-squared: 0.775, Adjusted R-squared: 0.7684
F-statistic: 117.1 on 1 and 34 DF, p-value: 1.485e-12
df_merged_m <- add_predictions(ols0, df_merged_m, "predicted_sales0")
# Model 1: Trend + Seasonality
ols1 <- run_model(sales_m ~ numeric_month + seasonal_month, df_merged_m, "Model 1")
Running Model 1
Call:
lm(formula = formula, data = data)
Residuals:
Min 1Q Median 3Q Max
-0.7403 -0.1590 -0.0135 0.2071 0.4347
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 16.505470 0.260998 63.240 < 2e-16
numeric_month 0.657412 0.075865 8.666 1.06e-08
seasonal_monthFebruary -0.001699 0.254032 -0.007 0.995
seasonal_monthMarch -0.006230 0.254345 -0.024 0.981
seasonal_monthApril -0.063031 0.254777 -0.247 0.807
seasonal_monthMay 0.070611 0.255288 0.277 0.785
seasonal_monthJune 0.037438 0.255855 0.146 0.885
seasonal_monthJuly 0.138742 0.256462 0.541 0.594
seasonal_monthAugust -0.010812 0.257098 -0.042 0.967
seasonal_monthSeptember -0.133330 0.257755 -0.517 0.610
seasonal_monthOctober -0.058397 0.258427 -0.226 0.823
seasonal_monthNovember -0.335279 0.254924 -1.315 0.201
seasonal_monthDecember -0.016084 0.254094 -0.063 0.950
(Intercept) ***
numeric_month ***
seasonal_monthFebruary
seasonal_monthMarch
seasonal_monthApril
seasonal_monthMay
seasonal_monthJune
seasonal_monthJuly
seasonal_monthAugust
seasonal_monthSeptember
seasonal_monthOctober
seasonal_monthNovember
seasonal_monthDecember
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.311 on 23 degrees of freedom
Multiple R-squared: 0.8123, Adjusted R-squared: 0.7144
F-statistic: 8.296 on 12 and 23 DF, p-value: 8.937e-06
df_merged_m <- add_predictions(ols1, df_merged_m, "predicted_sales1")
## Model 2: Backward Stepwise Regression
# Start with the full model (excluding food and bar)
ols2_full <- lm(
sales_m ~ numeric_month + seasonal_month + unemployment + ise + fx_m +
google_m + temp_m + rain_m,
data = df_merged_m
)
# Perform backward stepwise regression
ols2_stepwise <- step(
ols2_full,
direction = "backward",
trace = 1 # Prints the stepwise regression process
)
Start: AIC=-105.33
sales_m ~ numeric_month + seasonal_month + unemployment + ise +
fx_m + google_m + temp_m + rain_m
Df Sum of Sq RSS AIC
- unemployment 1 0.00381 0.67561 -107.124
- temp_m 1 0.01925 0.69105 -106.310
<none> 0.67180 -105.327
- rain_m 1 0.09618 0.76798 -102.510
- seasonal_month 11 0.79857 1.47037 -99.128
- ise 1 0.17973 0.85153 -98.793
- fx_m 1 0.44902 1.12082 -88.900
- google_m 1 0.66138 1.33318 -82.654
- numeric_month 1 2.42351 3.09530 -52.331
Step: AIC=-107.12
sales_m ~ numeric_month + seasonal_month + ise + fx_m + google_m +
temp_m + rain_m
Df Sum of Sq RSS AIC
- temp_m 1 0.03858 0.7142 -107.125
<none> 0.6756 -107.124
- rain_m 1 0.12563 0.8012 -102.984
- seasonal_month 11 0.80318 1.4788 -100.923
- ise 1 0.17592 0.8515 -100.793
- fx_m 1 0.46250 1.1381 -90.349
- google_m 1 0.65864 1.3343 -84.625
- numeric_month 1 3.11738 3.7930 -47.013
Step: AIC=-107.12
sales_m ~ numeric_month + seasonal_month + ise + fx_m + google_m +
rain_m
Df Sum of Sq RSS AIC
<none> 0.7142 -107.125
- rain_m 1 0.0940 0.8082 -104.673
- seasonal_month 11 0.7847 1.4989 -102.437
- ise 1 0.1606 0.8748 -101.823
- fx_m 1 0.4343 1.1485 -92.022
- google_m 1 0.6466 1.3608 -85.916
- numeric_month 1 4.1118 4.8260 -40.342
# Summary of the final stepwise model
summary(ols2_stepwise)
Call:
lm(formula = sales_m ~ numeric_month + seasonal_month + ise +
fx_m + google_m + rain_m, data = df_merged_m)
Residuals:
Min 1Q Median 3Q Max
-0.31229 -0.08760 -0.01030 0.09029 0.31789
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -52.31160 19.99397 -2.616 0.016981
numeric_month 0.93626 0.08952 10.459 2.54e-09
seasonal_monthFebruary 0.27615 0.19812 1.394 0.179459
seasonal_monthMarch -0.33136 0.28825 -1.150 0.264583
seasonal_monthApril -0.03032 0.20910 -0.145 0.886232
seasonal_monthMay -0.12629 0.27633 -0.457 0.652850
seasonal_monthJune -0.16788 0.27401 -0.613 0.547361
seasonal_monthJuly -0.11655 0.30708 -0.380 0.708483
seasonal_monthAugust -0.45680 0.33544 -1.362 0.189189
seasonal_monthSeptember -0.40348 0.27930 -1.445 0.164861
seasonal_monthOctober -0.21625 0.28064 -0.771 0.450439
seasonal_monthNovember -0.67606 0.38426 -1.759 0.094603
seasonal_monthDecember -1.52898 0.67026 -2.281 0.034247
ise 7.20920 3.48786 2.067 0.052641
fx_m 2.72323 0.80115 3.399 0.003010
google_m 3.17853 0.76636 4.148 0.000547
rain_m -0.20297 0.12835 -1.581 0.130285
(Intercept) *
numeric_month ***
seasonal_monthFebruary
seasonal_monthMarch
seasonal_monthApril
seasonal_monthMay
seasonal_monthJune
seasonal_monthJuly
seasonal_monthAugust
seasonal_monthSeptember
seasonal_monthOctober
seasonal_monthNovember .
seasonal_monthDecember *
ise .
fx_m **
google_m ***
rain_m
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.1939 on 19 degrees of freedom
Multiple R-squared: 0.9397, Adjusted R-squared: 0.889
F-statistic: 18.52 on 16 and 19 DF, p-value: 2.609e-08
# Add predictions from the final stepwise model
df_merged_m <- add_predictions(ols2_stepwise, df_merged_m, "predicted_sales2")
# Plot Actual vs Predicted Values
ggplot(df_merged_m, aes(x = month)) +
geom_line(aes(y = exp(sales_m), color = "Actual Sales"), size = 1) +
geom_line(aes(y = exp(predicted_sales0), color = "Model 0"), linetype = "dashed", size = 1) +
geom_line(aes(y = exp(predicted_sales1), color = "Model 1"), linetype = "dotted", size = 1) +
geom_line(aes(y = exp(predicted_sales2), color = "Model 2 Stepwise"), linetype = "dotdash", size = 1) +
labs(title = "Actual vs Predicted Monthly Sales for All Models",
x = "Month", y = "Sales", color = "Legend") +
theme_minimal() +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
# Models to compare
models <- list(
"Model trend" = ols0,
"Model trend + season" = ols1,
"Model all covariates step" = ols2_stepwise
)
# Get R^2 and AIC for each model
model_stats <- get_model_stats(models)
# View the results
print(model_stats)
# RMSE calculation for the original (exponentiated) scale
rmse_stats <- data.frame(
Model = character(),
RMSE = numeric(),
stringsAsFactors = FALSE
)
# Loop through each model
for (i in seq_along(models)) {
model_name <- names(models)[i]
predicted_column <- paste0("predicted_sales", i - 1) # Adjust column name index
# Calculate RMSE on the original scale
rmse <- calculate_rmse(
observed = exp(df_merged_m$sales_m), # Exponentiate actual values
predicted = exp(df_merged_m[[predicted_column]]) # Exponentiate predicted values
)
# Append results to the RMSE stats table
rmse_stats <- rbind(rmse_stats, data.frame(Model = model_name, RMSE = rmse))
}
# View RMSE statistics
print(rmse_stats)
NA
rmse_ols_m <- rmse_stats$RMSE[3]
rmse_ols_m
[1] 13229295
# Weekly Models
head(df_merged_w)
## Clean Data - Drop rows 1-2 because sales are 0 / was not open yet
df_merged_w <- df_merged_w %>% slice(-1, -2)
## Model 0A: Trend only
ols0w <- run_model(sales_w ~ numeric_week, df_merged_w, "Model 0A")
Running Model 0A
Call:
lm(formula = formula, data = data)
Residuals:
Min 1Q Median 3Q Max
-0.79976 -0.15274 0.02907 0.15945 0.62620
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 14.78396 0.10486 140.99 <2e-16 ***
numeric_week 0.49907 0.02464 20.25 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.232 on 151 degrees of freedom
Multiple R-squared: 0.7309, Adjusted R-squared: 0.7291
F-statistic: 410.2 on 1 and 151 DF, p-value: < 2.2e-16
df_merged_w <- add_predictions(ols0w, df_merged_w, "predicted_sales0")
## Model 1A: Trend + Seasonality
ols1w <- run_model(sales_w ~ numeric_week + seasonal_month, df_merged_w, "Model 1A")
Running Model 1A
Call:
lm(formula = formula, data = data)
Residuals:
Min 1Q Median 3Q Max
-0.67646 -0.14198 0.01153 0.15503 0.55098
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 14.80670 0.11510 128.640 <2e-16 ***
numeric_week 0.49526 0.02589 19.132 <2e-16 ***
seasonal_monthFebruary 0.02570 0.09019 0.285 0.776
seasonal_monthMarch -0.06118 0.08865 -0.690 0.491
seasonal_monthApril -0.02874 0.08878 -0.324 0.747
seasonal_monthMay 0.06556 0.08879 0.738 0.462
seasonal_monthJune 0.05271 0.08948 0.589 0.557
seasonal_monthJuly 0.11376 0.08777 1.296 0.197
seasonal_monthAugust -0.01542 0.09172 -0.168 0.867
seasonal_monthSeptember -0.09398 0.09038 -1.040 0.300
seasonal_monthOctober -0.05580 0.08864 -0.629 0.530
seasonal_monthNovember 0.07442 0.09812 0.758 0.449
seasonal_monthDecember -0.13767 0.08816 -1.562 0.121
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.2289 on 140 degrees of freedom
Multiple R-squared: 0.7571, Adjusted R-squared: 0.7362
F-statistic: 36.36 on 12 and 140 DF, p-value: < 2.2e-16
df_merged_w <- add_predictions(ols1w, df_merged_w, "predicted_sales1")
## Model 2A: Experimentation
# Start with the full model (excluding food and bar)
ols2_full_w <- lm(
sales_w ~ numeric_week + seasonal_month + fx_w +
google_w + temp_w + rain_w,
data = df_merged_w
)
# Perform backward stepwise regression
ols2_stepwise_w <- step(
ols2_full_w,
direction = "backward",
trace = 1 # Prints the stepwise regression process
)
Start: AIC=-474.75
sales_w ~ numeric_week + seasonal_month + fx_w + google_w + temp_w +
rain_w
Df Sum of Sq RSS AIC
- google_w 1 0.0017 5.5046 -476.70
- temp_w 1 0.0288 5.5317 -475.95
<none> 5.5028 -474.75
- rain_w 1 0.2315 5.7343 -470.45
- seasonal_month 11 1.2581 6.7609 -465.25
- fx_w 1 1.3796 6.8825 -442.52
- numeric_week 1 11.9715 17.4743 -299.96
Step: AIC=-476.7
sales_w ~ numeric_week + seasonal_month + fx_w + temp_w + rain_w
Df Sum of Sq RSS AIC
- temp_w 1 0.0281 5.5327 -477.92
<none> 5.5046 -476.70
- rain_w 1 0.2325 5.7370 -472.38
- seasonal_month 11 1.2566 6.7612 -467.24
- fx_w 1 1.4037 6.9082 -443.95
- numeric_week 1 15.3205 20.8251 -275.12
Step: AIC=-477.92
sales_w ~ numeric_week + seasonal_month + fx_w + rain_w
Df Sum of Sq RSS AIC
<none> 5.5327 -477.92
- rain_w 1 0.2056 5.7384 -474.34
- seasonal_month 11 1.2336 6.7663 -469.13
- fx_w 1 1.3879 6.9206 -445.68
- numeric_week 1 16.3743 21.9070 -269.38
# Summary of the final stepwise model
summary(ols2_stepwise_w)
Call:
lm(formula = sales_w ~ numeric_week + seasonal_month + fx_w +
rain_w, data = df_merged_w)
Residuals:
Min 1Q Median 3Q Max
-0.6258 -0.1168 0.0029 0.1220 0.5414
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.795973 2.529046 -0.315 0.7534
numeric_week 0.514279 0.025448 20.209 < 2e-16
seasonal_monthFebruary 0.009356 0.079421 0.118 0.9064
seasonal_monthMarch -0.002569 0.078234 -0.033 0.9739
seasonal_monthApril 0.064014 0.081105 0.789 0.4313
seasonal_monthMay 0.165794 0.082132 2.019 0.0455
seasonal_monthJune 0.179993 0.085195 2.113 0.0364
seasonal_monthJuly 0.153995 0.077211 1.994 0.0481
seasonal_monthAugust 0.001588 0.080384 0.020 0.9843
seasonal_monthSeptember -0.108556 0.079833 -1.360 0.1761
seasonal_monthOctober -0.092775 0.078684 -1.179 0.2404
seasonal_monthNovember 0.088688 0.091541 0.969 0.3343
seasonal_monthDecember -0.099444 0.078197 -1.272 0.2056
fx_w 1.976626 0.335948 5.884 2.89e-08
rain_w -0.115589 0.051037 -2.265 0.0251
(Intercept)
numeric_week ***
seasonal_monthFebruary
seasonal_monthMarch
seasonal_monthApril
seasonal_monthMay *
seasonal_monthJune *
seasonal_monthJuly *
seasonal_monthAugust
seasonal_monthSeptember
seasonal_monthOctober
seasonal_monthNovember
seasonal_monthDecember
fx_w ***
rain_w *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.2002 on 138 degrees of freedom
Multiple R-squared: 0.8167, Adjusted R-squared: 0.7982
F-statistic: 43.93 on 14 and 138 DF, p-value: < 2.2e-16
# Add predictions from the final stepwise model
df_merged_w <- add_predictions(ols2_stepwise_w, df_merged_w, "predicted_sales2")
# Plot Actual vs Predicted Values
ggplot(df_merged_w, aes(x = week)) +
geom_line(aes(y = exp(sales_w), color = "Actual Sales"), size = 1) +
geom_line(aes(y = exp(predicted_sales0), color = "Model 0"), linetype = "dashed", size = 1) +
geom_line(aes(y = exp(predicted_sales1), color = "Model 1"), linetype = "dotted", size = 1) +
geom_line(aes(y = exp(predicted_sales2), color = "Model 2 Stepwise"), linetype = "dotdash", size = 1) +
labs(title = "Actual vs Predicted Weekly Sales for All Models",
x = "Week", y = "Sales", color = "Legend") +
theme_minimal() +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
# Models to compare
models_w <- list(
"Model trend" = ols0w,
"Model trend + season" = ols1w,
"Model all covariates step" = ols2_stepwise_w
)
# Get R^2 and AIC for each model
model_stats_w <- get_model_stats(models_w)
# View the results
print(model_stats_w)
rmse_stats_w <- data.frame(
Model = character(),
RMSE = numeric(),
stringsAsFactors = FALSE
)
# Loop through each model
for (i in seq_along(models_w)) {
model_name <- names(models_w)[i]
predicted_column <- paste0("predicted_sales", i - 1) # Adjust column name index
# Calculate RMSE on the original scale
rmse <- calculate_rmse(
observed = exp(df_merged_w$sales_w), # Exponentiate actual values
predicted = exp(df_merged_w[[predicted_column]]) # Exponentiate predicted values
)
# Append results to the RMSE stats table
rmse_stats_w <- rbind(rmse_stats_w, data.frame(Model = model_name, RMSE = rmse))
}
# View RMSE statistics
print(rmse_stats_w)
NA
rmse_ols_w <- rmse_stats_w$RMSE[3]
rmse_ols_w
[1] 3909103
# Daily Models
head(df_merged_d,25)
# properly start in december
df_merged_d <- df_merged_d %>%
filter(date > "2021-11-30")
head(df_merged_d)
## Model 0: Trend only
ols0d <- run_model(sales_cop ~ numeric_day, df_merged_d, "Model 0A")
Running Model 0A
Call:
lm(formula = formula, data = data)
Residuals:
Min 1Q Median 3Q Max
-15.2118 -0.1833 0.2033 0.5788 1.6889
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 10.4838 0.4287 24.456 <2e-16 ***
numeric_day 0.6831 0.0699 9.772 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.762 on 1037 degrees of freedom
Multiple R-squared: 0.08432, Adjusted R-squared: 0.08344
F-statistic: 95.5 on 1 and 1037 DF, p-value: < 2.2e-16
df_merged_d <- add_predictions(ols0d, df_merged_d, "predicted_sales0")
## Model 1: Trend + Seasonality
ols1d <- run_model(sales_cop ~ numeric_day + seasonal_month + day_of_week, df_merged_d, "Model 1A")
Running Model 1A
Call:
lm(formula = formula, data = data)
Residuals:
Min 1Q Median 3Q Max
-15.1961 -0.1426 0.1547 0.4376 2.2118
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 10.36800 0.46988 22.065 < 2e-16 ***
numeric_day 0.61107 0.07316 8.353 < 2e-16 ***
seasonal_monthFebruary 0.37605 0.26287 1.431 0.15286
seasonal_monthMarch 0.24022 0.25678 0.936 0.34975
seasonal_monthApril 0.21367 0.26029 0.821 0.41191
seasonal_monthMay 0.03355 0.25766 0.130 0.89643
seasonal_monthJune 0.15004 0.26178 0.573 0.56666
seasonal_monthJuly 0.22890 0.25938 0.882 0.37773
seasonal_monthAugust 0.24650 0.26028 0.947 0.34383
seasonal_monthSeptember -0.04394 0.26445 -0.166 0.86806
seasonal_monthOctober 0.22407 0.26395 0.849 0.39615
seasonal_monthNovember 0.05368 0.29619 0.181 0.85622
seasonal_monthDecember -0.71696 0.25824 -2.776 0.00560 **
day_of_weekTuesday -0.07884 0.19861 -0.397 0.69148
day_of_weekWednesday 0.22688 0.19767 1.148 0.25133
day_of_weekThursday 0.47554 0.19734 2.410 0.01614 *
day_of_weekFriday 1.10956 0.19862 5.586 2.97e-08 ***
day_of_weekSaturday 0.93771 0.19827 4.730 2.57e-06 ***
day_of_weekSunday 0.61578 0.19825 3.106 0.00195 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.705 on 1020 degrees of freedom
Multiple R-squared: 0.1565, Adjusted R-squared: 0.1417
F-statistic: 10.52 on 18 and 1020 DF, p-value: < 2.2e-16
df_merged_d <- add_predictions(ols1d, df_merged_d, "predicted_sales1")
# Model 2: Backward
head(df_merged_d)
# Start with the full model (excluding food and bar)
ols2_full_d <- lm(
sales_cop ~ numeric_day + seasonal_month + day_of_week + fx +
tmedian + rain_sum,
data = df_merged_d
)
summary(ols2_full_d)
Call:
lm(formula = sales_cop ~ numeric_day + seasonal_month + day_of_week +
fx + tmedian + rain_sum, data = df_merged_d)
Residuals:
Min 1Q Median 3Q Max
-15.2636 -0.1276 0.1461 0.4151 2.2576
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.279201 7.571387 0.433 0.66503
numeric_day 0.565330 0.079450 7.116 2.10e-12
seasonal_monthFebruary 0.406952 0.263751 1.543 0.12316
seasonal_monthMarch 0.252562 0.257085 0.982 0.32613
seasonal_monthApril 0.213593 0.264546 0.807 0.41963
seasonal_monthMay -0.001365 0.263002 -0.005 0.99586
seasonal_monthJune 0.122006 0.268559 0.454 0.64971
seasonal_monthJuly 0.224695 0.260074 0.864 0.38781
seasonal_monthAugust 0.277725 0.260743 1.065 0.28707
seasonal_monthSeptember -0.003025 0.265704 -0.011 0.99092
seasonal_monthOctober 0.143398 0.266198 0.539 0.59022
seasonal_monthNovember -0.132339 0.305424 -0.433 0.66489
seasonal_monthDecember -0.742806 0.258943 -2.869 0.00421
day_of_weekTuesday -0.075196 0.198313 -0.379 0.70464
day_of_weekWednesday 0.238097 0.197517 1.205 0.22831
day_of_weekThursday 0.472214 0.197048 2.396 0.01673
day_of_weekFriday 1.102508 0.198311 5.559 3.46e-08
day_of_weekSaturday 0.930469 0.197993 4.699 2.97e-06
day_of_weekSunday 0.615183 0.198117 3.105 0.00195
fx 0.827866 0.881531 0.939 0.34789
tmedian -0.135956 0.999284 -0.136 0.89181
rain_sum 0.136200 0.101044 1.348 0.17798
(Intercept)
numeric_day ***
seasonal_monthFebruary
seasonal_monthMarch
seasonal_monthApril
seasonal_monthMay
seasonal_monthJune
seasonal_monthJuly
seasonal_monthAugust
seasonal_monthSeptember
seasonal_monthOctober
seasonal_monthNovember
seasonal_monthDecember **
day_of_weekTuesday
day_of_weekWednesday
day_of_weekThursday *
day_of_weekFriday ***
day_of_weekSaturday ***
day_of_weekSunday **
fx
tmedian
rain_sum
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.702 on 1017 degrees of freedom
Multiple R-squared: 0.1618, Adjusted R-squared: 0.1445
F-statistic: 9.349 on 21 and 1017 DF, p-value: < 2.2e-16
# Perform backward stepwise regression
ols2_stepwise_d <- step(
ols2_full_d,
direction = "backward",
trace = 1 # Prints the stepwise regression process
)
Start: AIC=1127.38
sales_cop ~ numeric_day + seasonal_month + day_of_week + fx +
tmedian + rain_sum
Df Sum of Sq RSS AIC
- tmedian 1 0.054 2947.6 1125.4
- fx 1 2.556 2950.1 1126.3
- rain_sum 1 5.266 2952.8 1127.2
<none> 2947.6 1127.4
- seasonal_month 11 79.060 3026.6 1132.9
- numeric_day 1 146.743 3094.3 1175.9
- day_of_week 6 177.279 3124.8 1176.1
Step: AIC=1125.4
sales_cop ~ numeric_day + seasonal_month + day_of_week + fx +
rain_sum
Df Sum of Sq RSS AIC
- fx 1 2.515 2950.1 1124.3
<none> 2947.6 1125.4
- rain_sum 1 5.915 2953.5 1125.5
- seasonal_month 11 79.341 3026.9 1131.0
- day_of_week 6 177.262 3124.9 1174.1
- numeric_day 1 149.907 3097.5 1174.9
Step: AIC=1124.29
sales_cop ~ numeric_day + seasonal_month + day_of_week + rain_sum
Df Sum of Sq RSS AIC
<none> 2950.1 1124.3
- rain_sum 1 15.917 2966.0 1127.9
- seasonal_month 11 78.865 3029.0 1129.7
- day_of_week 6 176.760 3126.9 1172.7
- numeric_day 1 147.563 3097.7 1173.0
# Summary of the final stepwise model
summary(ols2_stepwise_d)
Call:
lm(formula = sales_cop ~ numeric_day + seasonal_month + day_of_week +
rain_sum, data = df_merged_d)
Residuals:
Min 1Q Median 3Q Max
-15.1848 -0.1398 0.1461 0.4324 2.3762
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 9.49003 0.60001 15.816 < 2e-16 ***
numeric_day 0.55165 0.07727 7.139 1.78e-12 ***
seasonal_monthFebruary 0.42084 0.26299 1.600 0.10986
seasonal_monthMarch 0.23726 0.25622 0.926 0.35466
seasonal_monthApril 0.17038 0.26037 0.654 0.51301
seasonal_monthMay -0.03721 0.25886 -0.144 0.88573
seasonal_monthJune 0.07280 0.26327 0.277 0.78220
seasonal_monthJuly 0.20776 0.25897 0.802 0.42259
seasonal_monthAugust 0.27190 0.25993 1.046 0.29579
seasonal_monthSeptember 0.01008 0.26487 0.038 0.96964
seasonal_monthOctober 0.16643 0.26452 0.629 0.52938
seasonal_monthNovember -0.12439 0.30514 -0.408 0.68362
seasonal_monthDecember -0.74920 0.25804 -2.903 0.00377 **
day_of_weekTuesday -0.07454 0.19818 -0.376 0.70690
day_of_weekWednesday 0.24211 0.19734 1.227 0.22017
day_of_weekThursday 0.47096 0.19691 2.392 0.01695 *
day_of_weekFriday 1.10237 0.19820 5.562 3.41e-08 ***
day_of_weekSaturday 0.92890 0.19787 4.695 3.04e-06 ***
day_of_weekSunday 0.61671 0.19782 3.118 0.00187 **
rain_sum 0.19036 0.08119 2.345 0.01923 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.702 on 1019 degrees of freedom
Multiple R-squared: 0.1611, Adjusted R-squared: 0.1454
F-statistic: 10.3 on 19 and 1019 DF, p-value: < 2.2e-16
# Add predictions from the final stepwise model
df_merged_d <- add_predictions(ols2_stepwise_d, df_merged_d, "predicted_sales2")
# Plot Actual vs Predicted Values
ggplot(df_merged_d, aes(x = date)) +
geom_line(aes(y = exp(sales_cop), color = "Actual Sales"), size = 1) +
geom_line(aes(y = exp(predicted_sales0), color = "Model 0"), linetype = "dashed", size = 1) +
geom_line(aes(y = exp(predicted_sales1), color = "Model 1"), linetype = "dotted", size = 1) +
geom_line(aes(y = exp(predicted_sales2), color = "Model 2 Stepwise"), linetype = "dotdash", size = 1) +
labs(title = "Actual vs Predicted Sales for All Models",
x = "date", y = "Sales", color = "Legend") +
theme_minimal() +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
# Models to compare
models_d <- list(
"Model trend" = ols0d,
"Model trend + season" = ols1d,
"Model all covariates step" = ols2_stepwise_d
)
# Get R^2 and AIC for each model
model_stats_d <- get_model_stats(models_d)
# View the results
print(model_stats_d)
# RMSE calculation for the original (exponentiated) scale for daily models
rmse_stats_d <- data.frame(
Model = character(),
RMSE = numeric(),
stringsAsFactors = FALSE
)
# Loop through each model
for (i in seq_along(models_d)) {
model_name <- names(models_d)[i]
predicted_column <- paste0("predicted_sales", i - 1) # Adjust column name index
# Calculate RMSE on the original scale
rmse <- calculate_rmse(
observed = exp(df_merged_d$sales_cop), # Exponentiate actual values
predicted = exp(df_merged_d[[predicted_column]]) # Exponentiate predicted values
)
# Append results to the RMSE stats table
rmse_stats_d <- rbind(rmse_stats_d, data.frame(Model = model_name, RMSE = rmse))
}
# View RMSE statistics for daily data
print(rmse_stats_d)
rmse_ols_d <- rmse_stats_d$RMSE[3]
rmse_ols_d
[1] 1425907
Here we explore non linear models, starting from the simplest to more elaborate models in the end combining some of the used models.
The time series are altered so the visualizations are more understandable, basically we change the date index in the timeseries objects
# re-declare time-series beacause we droped some rows:
# Ensure the 'date' columns are in Date format
df_merged_d$date <- as.Date(df_merged_d$date)
df_merged_w$date <- as.Date(df_merged_w$week)
df_merged_m$date <- as.Date(df_merged_m$month)
# Extract the start date and year for each dataframe
start_d <- min(df_merged_d$date)
start_w <- min(df_merged_w$date)
start_m <- min(df_merged_m$date)
# Extract components for daily, weekly, and monthly start times
start_d_year <- as.numeric(format(start_d, "%Y"))
start_d_day <- as.numeric(format(start_d, "%j")) # Day of the year
start_w_year <- as.numeric(format(start_w, "%Y"))
start_w_week <- as.numeric(format(start_w, "%U")) + 1 # Week number, adding 1 since R starts at week 0
start_m_year <- as.numeric(format(start_m, "%Y"))
start_m_month <- as.numeric(format(start_m, "%m"))
# Declare time series with appropriate frequencies
sales_d_ts <- ts(exp(df_merged_d$sales_cop), start = c(start_d_year, start_d_day), frequency = 365)
sales_w_ts <- ts(exp(df_merged_w$sales_w), start = c(start_w_year, start_w_week), frequency = 52)
sales_m_ts <- ts(exp(df_merged_m$sales_m), start = c(start_m_year, start_m_month), frequency = 12)
food_d_ts <- ts(exp(df_merged_d$food), start = c(start_d_year, start_d_day), frequency = 365)
food_w_ts <- ts(exp(df_merged_w$food_w), start = c(start_w_year, start_w_week), frequency = 52)
food_m_ts <- ts(exp(df_merged_m$food_m), start = c(start_m_year, start_m_month), frequency = 12)
bar_d_ts <- ts(exp(df_merged_d$bar), start = c(start_d_year, start_d_day), frequency = 365)
bar_w_ts <- ts(exp(df_merged_w$bar_w), start = c(start_w_year, start_w_week), frequency = 52)
bar_m_ts <- ts(exp(df_merged_m$bar_m), start = c(start_m_year, start_m_month), frequency = 12)
# Verify the created time series
par(mfrow=c(1,1))
plot(sales_d_ts)
plot(sales_w_ts)
plot(sales_m_ts)
plot(food_d_ts)
plot(food_w_ts)
plot(food_m_ts)
plot(bar_d_ts)
plot(bar_w_ts)
plot(bar_m_ts)
Here we fill the sales = 0 values with the mean of the two adjacent dates. This in order to have smoother models. The dates with sales = 0 are dates that are national holiday like christmas or new years, or inventory day in which the kitchen cannot operate so the sales are 0.
# Function to replace 1s with the mean of previous and next observations
fill_ones <- function(ts_data) {
# Convert time series to numeric vector
ts_vec <- as.numeric(ts_data)
# Loop through and replace 1s
for (i in seq_along(ts_vec)) {
if (ts_vec[i] == 1) {
# Check boundaries to avoid indexing issues
prev_val <- ifelse(i > 1, ts_vec[i - 1], NA)
next_val <- ifelse(i < length(ts_vec), ts_vec[i + 1], NA)
# Replace with mean of previous and next, ignoring NA
ts_vec[i] <- mean(c(prev_val, next_val), na.rm = TRUE)
}
}
# Return as time series with original attributes
ts(ts_vec, start = start(ts_data), frequency = frequency(ts_data))
}
# Apply the function
sales_d_ts <- fill_ones(sales_d_ts)
sales_w_ts <- fill_ones(sales_w_ts)
sales_m_ts <- fill_ones(sales_m_ts)
food_d_ts <- fill_ones(food_d_ts)
food_w_ts <- fill_ones(food_w_ts)
food_m_ts <- fill_ones(food_m_ts)
bar_d_ts <- fill_ones(bar_d_ts)
bar_w_ts <- fill_ones(bar_w_ts)
bar_m_ts <- fill_ones(bar_m_ts)
# Some simple plots
plot(sales_m_ts)
plot(cumsum(sales_m_ts)) #Returns a vector whose elements are the cumulative sums
# Bass model
bm_m<-BM(sales_m_ts,display = T) # show graphical view of results / display = True
summary(bm_m)
Call: ( Standard Bass Model )
BM(series = sales_m_ts, display = T)
Residuals:
Min. 1st Qu. Median Mean 3rd Qu. Max.
-94382506 -37311459 -12636337 -10394220 24066002 75506534
Coefficients:
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error 47282474 on 33 degrees of freedom
Multiple R-squared: 0.999374 Residual sum of squares: 7.377587e+16
bm_m$coefficients['m'] - sum(sales_m_ts)
m
1148560231
According to this, there are only 1m cop left to sell, this is less than a year / seems wrong. Fits well but the 30- onward is wierd + sales might not be declining yet. Still reflects the innovation and copying in some sense
Also the restaurants rely in word of mouth to reach full stage m = 4.664.000.000 COP, i.e 1 mm EUR approx. / The restaurant has sold 3.515.788.885/ According to this only in 1 year it should extinguish sells p, innovation: 0.832% indicates that the adoption rate due to external influence is relatively low, but not uncommon for many markets. - it is actually relativly innovative q: (8.96%) suggests that imitation plays a larger role than innovation in driving adoption in this market
pred_bm_m<- predict(bm_m, newx=c(1:length(sales_m_ts)))
pred_bm_m <- ts(pred_bm_m, start = start(sales_m_ts), frequency = frequency(sales_m_ts))
pred.inst_bm_m <- make.instantaneous(pred_bm_m)
pred.inst_bm_m <- ts(pred.inst_bm_m, start = start(sales_m_ts), frequency = frequency(sales_m_ts))
# plot
plot(sales_m_ts, type = "p", col = "black", pch = 16, cex = 0.7,
xlab = "Month", ylab = "Monthly Sales", main = "Actual vs Fitted Sales")
# Add the fitted values as a line
lines(pred.inst_bm_m, col = "red", lwd = 2)
# Add a legend
legend("topleft", legend = c("Actual Values", "Fitted Values"),
col = c("black", "red"), pch = c(16, NA), lty = c(NA, 1), lwd = c(NA, 2))
# check residuals
res_bm_m <- sales_m_ts - pred.inst_bm_m
tsdisplay(res_bm_m)
Residuals have some structure and 2 lag has correlation.
# Calculate RMSE for Bass Model predictions
rmse_bm_m <- calculate_rmse(observed = sales_m_ts, predicted = pred.inst_bm_m)
# Print the RMSE
cat("RMSE for Bass Model Predictions:", rmse_bm_m, "\n")
RMSE for Bass Model Predictions: 18498870
bm_w<-BM(sales_w_ts,display = T) # show graphical view of results / display = True
summary(bm_w)
bm_w$coefficients['m'] - sum(sales_w_ts)
# results are similar in terms of m, p and w are in other scale
#because they are in different time stamp
bm_m$coefficients['q'] / bm_w$coefficients['q'] # they are approx 4 times
bm_m$coefficients['p'] / bm_w$coefficients['p'] # they are approx 4 times
# which makes sense
Coefficients are approximatly 4 times the ones of the monthly model, making sense because there are 4 weeks in a month. While market potential is similar.
# Prediction
pred_bm_w<- predict(bm_w, newx=c(1:length(sales_w_ts)))
pred_bm_w <- ts(pred_bm_w, start = start(sales_w_ts), frequency = frequency(sales_w_ts))
pred.inst_bm_w <- make.instantaneous(pred_bm_w)
pred.inst_bm_w <- ts(pred.inst_bm_w, start = start(sales_w_ts), frequency = frequency(sales_w_ts))
# plot
plot(sales_w_ts, type = "p", col = "black", pch = 16, cex = 0.7,
xlab = "Week", ylab = "Weekly Sales", main = "Actual vs Fitted Sales")
# Add the fitted values as a line
lines(pred.inst_bm_w, col = "red", lwd = 2)
# Add a legend
legend("topleft", legend = c("Actual Values", "Fitted Values"),
col = c("black", "red"), pch = c(16, NA), lty = c(NA, 1), lwd = c(NA, 2))
# check residuals
res_bm_w <- sales_w_ts - pred.inst_bm_w
tsdisplay(res_bm_w)
Residuals have some structure and 2 lag has correlation, with clear trend and structure in the residuals
# RMSE
# Calculate RMSE for Bass Model predictions
rmse_bm_w <- calculate_rmse(observed = sales_w_ts, predicted = pred.inst_bm_w)
# Print the RMSE
cat("RMSE for Bass Model Predictions:", rmse_bm_w, "\n")
bm_d <- BM(
sales_d_ts,
prelimestimates = c(1.2 * sum(sales_d_ts), 0.005, 0.5), # Adjust these estimates
display = TRUE
)
summary(bm_d)
bm_d$coefficients['m'] - sum(sales_d_ts)
# results are similar in terms of m, p and w are in other scale
#because they are in different time stamp
bm_w$coefficients['q'] / bm_d$coefficients['q'] # they are approx 7 times
bm_w$coefficients['p'] / bm_d$coefficients['p'] # they are approx 7 times
Coefficients are approximately 1:7 scale of the ones in the weekly model, making sense. The market potential is also similar in order of magnitude.
# Prediction
pred_bm_d <- predict(bm_d, newx = c(1:length(sales_d_ts)))
pred_bm_d <- ts(pred_bm_d, start = start(sales_d_ts), frequency = frequency(sales_d_ts))
pred.inst_bm_d <- make.instantaneous(pred_bm_d)
pred.inst_bm_d <- ts(pred.inst_bm_d, start = start(sales_d_ts), frequency = frequency(sales_d_ts))
# Plot actual vs fitted sales for daily data
plot(sales_d_ts, type = "p", col = "black", pch = 16, cex = 0.7,
xlab = "Day", ylab = "Daily Sales", main = "Actual vs Fitted Sales (Daily)")
# Add the fitted values as a line
lines(pred.inst_bm_d, col = "red", lwd = 2)
# Add a legend
legend("topleft", legend = c("Actual Values", "Fitted Values"),
col = c("black", "red"), pch = c(16, NA), lty = c(NA, 1), lwd = c(NA, 2))
# Check residuals
res_bm_d <- sales_d_ts - pred.inst_bm_d
tsdisplay(res_bm_d)
Residuals don not seem stationary, or at least they have a lot of autocorrelation.
# Calculate RMSE for Bass Model predictions (daily data)
rmse_bm_d <- calculate_rmse(observed = sales_d_ts, predicted = pred.inst_bm_d)
# Print the RMSE
cat("RMSE for Daily Bass Model Predictions:", rmse_bm_d, "\n")
Bass model assumes that every product succeeds and the sales saturate to the steady state level. However, most new products fail in reality.
The market potential m is constant along the whole life cycle.
Bass model predictions works well only after the scale inflection point. if sales of a category goes up and up like a J-curve, it can over estimate the overall market size.
It is a model for products with a limited life cycle: needs a hypothesis.
Another drawback of Bass model is that the diffusion pattern in not affected by marketing mix variables like price or advertising.
The generalized Bass model extends the original Bass model allowing the roles of marketing mix value.
Bass model is used to forecast the adoption of a new product and to predict the sales, since it determines the shape of the curve of a model that represent the cumulative adoption of a new product. The Generalized Bass model extends the original Bass model by incorporating marketing mix variables. We can know the effect of pricing, promotions on the new product diffusion curve. It is more flexible than the original Bass model.
m <- 4.451570e+09
p <- 8.472917e-03
q <- 9.415625e-02
GBM_monthly_sales <- GBM(
sales_m_ts,
shock = 'exp',
nshock = 1,
#prelimestimates = c(m,p,q, 12, 0.1, -0.1)
prelimestimates = c(m,p,q, 10, 0.1, 2)
#prelimestimates = c(m,p,q, 11, 15, -0.1)
)
summary(GBM_monthly_sales)
pred_GBM_monthly_sales<- predict(GBM_monthly_sales, newx=c(1:60))
pred_GBM_monthly_sales.inst<- make.instantaneous(pred_GBM_monthly_sales)
# Montly model
ggm1 <- GGM(sales_m_ts, mt='base', display = T)
Warning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs produced
ggm2 <- GGM(sales_m_ts, mt= function(x) pchisq(x,10),display = T)
summary(ggm1)
Call: ( Guseo Guidolin Model )
GGM(series = sales_m_ts, mt = "base", display = T)
Residuals:
Min. 1st Qu. Median Mean 3rd Qu. Max.
-27544719 -8809035 742251 -337148 7701034 23238738
Coefficients:
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error 13318300 on 31 degrees of freedom
Multiple R-squared: 0.999873 Residual sum of squares: 5.498691e+15
summary(ggm2)
Call: ( Guseo Guidolin Model )
GGM(series = sales_m_ts, mt = function(x) pchisq(x, 10), display = T)
Residuals:
Min. 1st Qu. Median Mean 3rd Qu. Max.
-55479254 -21799576 5818484 25726804 63528263 144216338
Coefficients:
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error 64933559 on 33 degrees of freedom
Multiple R-squared: 0.99678 Residual sum of squares: 1.391401e+17
# try different functions for market potential
ggm3 <- GGM(sales_m_ts, mt= function(x) log(x),display = T)
ggm4 <- GGM(sales_m_ts, mt= function(x) (x)**(1/1.05),display = T)
summary(ggm3)
Call: ( Guseo Guidolin Model )
GGM(series = sales_m_ts, mt = function(x) log(x), display = T)
Residuals:
Min. 1st Qu. Median Mean 3rd Qu. Max.
-51543377 -17143219 -1444208 -3434599 7197387 38682408
Coefficients:
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error 23487767 on 33 degrees of freedom
Multiple R-squared: 0.999579 Residual sum of squares: 1.820528e+16
summary(ggm4)
Call: ( Guseo Guidolin Model )
GGM(series = sales_m_ts, mt = function(x) (x)^(1/1.05), display = T)
Residuals:
Min. 1st Qu. Median Mean 3rd Qu. Max.
-33877044 -9900757 -986705 -1517515 10675797 29488516
Coefficients:
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error 16905824 on 33 degrees of freedom
Multiple R-squared: 0.999782 Residual sum of squares: 9.431627e+15
K <- 7.683785e+09
pc <- 2.698613e-02
qc <- 2.582412e-01
ps <- 7.731763e-03
qs <- 4.508202e-02
# predictions
pred_ggm_m <- predict(ggm1, newx = c(1:length(sales_m_ts)))
pred_ggm_m <- ts(pred_ggm_m, start = start(sales_m_ts), frequency = frequency(sales_m_ts))
pred.inst_ggm_m <- make.instantaneous(pred_ggm_m)
pred.inst_ggm_m <- ts(pred.inst_ggm_m, start = start(sales_m_ts), frequency = frequency(sales_m_ts))
# Plot actual vs fitted sales for monthly data
plot(sales_m_ts, type = "p", col = "black", pch = 16, cex = 0.7,
xlab = "Month", ylab = "Monthly Sales", main = "Actual vs Fitted Sales (GGM Model)")
# Add the fitted values as a line
lines(pred.inst_ggm_m, col = "red", lwd = 2)
# Add a legend
legend("topleft", legend = c("Actual Values", "Fitted Values (GGM)"),
col = c("black", "red"), pch = c(16, NA), lty = c(NA, 1), lwd = c(NA, 2))
#Analysis of residuals
res_GGM_m<- sales_m_ts - pred.inst_ggm_m
tsdisplay(res_GGM_m)
Residuals look stationary for this model
# Residuals somehow are kind of stationary
# check for stationarity of residuals
adf_test <- adf.test(res_GGM_m)
print(adf_test) # if p-val < alpha, series stationary
Augmented Dickey-Fuller Test
data: res_GGM_m
Dickey-Fuller = -4.1, Lag order = 3, p-value = 0.01708
alternative hypothesis: stationary
# so with this model we achieve stationary series
# check for autocorrelation in residuals
Box.test(res_GGM_m, lag = 10, type = "Ljung-Box") # h0 res indep
Box-Ljung test
data: res_GGM_m
X-squared = 16.263, df = 10, p-value = 0.09234
# p-val > alpha => fail to reject h0, so residuals seem indep
Residuals are likeley stationary
# Calculate RMSE for ggm1
rmse_ggm1 <- calculate_rmse(observed = sales_m_ts, predicted = pred.inst_ggm_m)
# Print RMSE for ggm1
cat("RMSE for GGM Model 1 (Base):", rmse_ggm1, "\n")
RMSE for GGM Model 1 (Base): 11759505
# Weekly
ggm1_w <- GGM(sales_w_ts, mt='base', display = T)
ggm2_w <- GGM(sales_w_ts, mt= function(x) pchisq(x,25),display = T)
summary(ggm1_w) # this one is better
Call: ( Guseo Guidolin Model )
GGM(series = sales_w_ts, mt = "base", display = T)
Residuals:
Min. 1st Qu. Median Mean 3rd Qu. Max.
-31498207 -8733958 2309014 276818 8889298 21142720
Coefficients:
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error 12329105 on 148 degrees of freedom
Multiple R-squared: 0.999873 Residual sum of squares: 2.249701e+16
summary(ggm2_w)
Call: ( Guseo Guidolin Model )
GGM(series = sales_w_ts, mt = function(x) pchisq(x, 25), display = T)
Residuals:
Min. 1st Qu. Median Mean 3rd Qu. Max.
-33750595 -17052328 2617278 9791490 29825798 107962582
Coefficients:
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error 36797065 on 150 degrees of freedom
Multiple R-squared: 0.998856 Residual sum of squares: 2.031036e+17
# try different functions for market potential
ggm3_w <- GGM(sales_w_ts, mt= function(x) log(x),display = T)
ggm4_w <- GGM(sales_w_ts, mt= function(x) (x)**(1/1.05),display = T)
summary(ggm3_w)
Call: ( Guseo Guidolin Model )
GGM(series = sales_w_ts, mt = function(x) log(x), display = T)
Residuals:
Min. 1st Qu. Median Mean 3rd Qu. Max.
-56356239 -18752252 -3739136 -3874766 8381947 42340483
Coefficients:
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error 23371927 on 150 degrees of freedom
Multiple R-squared: 0.999539 Residual sum of squares: 8.193705e+16
summary(ggm4_w) # better shaped but less significant
Call: ( Guseo Guidolin Model )
GGM(series = sales_w_ts, mt = function(x) (x)^(1/1.05), display = T)
Residuals:
Min. 1st Qu. Median Mean 3rd Qu. Max.
-33312923 -9281560 1900857 133074 10271969 26473496
Coefficients:
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error 13629605 on 150 degrees of freedom
Multiple R-squared: 0.999843 Residual sum of squares: 2.786492e+16
# predictions
pred_ggm_w <- predict(ggm1_w, newx = c(1:length(sales_w_ts)))
pred_ggm_w <- ts(pred_ggm_w, start = start(sales_w_ts), frequency = frequency(sales_w_ts))
pred.inst_ggm_w <- make.instantaneous(pred_ggm_w)
pred.inst_ggm_w <- ts(pred.inst_ggm_w, start = start(sales_w_ts), frequency = frequency(sales_w_ts))
# Plot actual vs fitted sales for weekly data
plot(sales_w_ts, type = "p", col = "black", pch = 16, cex = 0.7,
xlab = "Week", ylab = "Weekly Sales", main = "Actual vs Fitted Sales (GGM Model)")
# Add the fitted values as a line
lines(pred.inst_ggm_w, col = "red", lwd = 2)
# Add a legend
legend("topleft", legend = c("Actual Values", "Fitted Values (GGM)"),
col = c("black", "red"), pch = c(16, NA), lty = c(NA, 1), lwd = c(NA, 2))
# Analysis of residuals
res_GGM_w <- sales_w_ts - pred.inst_ggm_w
tsdisplay(res_GGM_w)
# Check for stationarity of residuals
adf_test_w <- adf.test(res_GGM_w)
Warning: p-value smaller than printed p-value
print(adf_test_w) # if p-value < alpha, series is stationary
Augmented Dickey-Fuller Test
data: res_GGM_w
Dickey-Fuller = -4.277, Lag order = 5, p-value = 0.01
alternative hypothesis: stationary
# Check for autocorrelation in residuals
box_test_w <- Box.test(res_GGM_w, lag = 10, type = "Ljung-Box")
print(box_test_w) # if p-value > alpha, residuals are independent
Box-Ljung test
data: res_GGM_w
X-squared = 54.208, df = 10, p-value = 4.437e-08
Series is stationary according to tests, but clearly has strong autocorrelation
# RMSE
rmse_ggm_w <- calculate_rmse(observed = sales_w_ts, predicted = pred.inst_ggm_w)
# Print the RMSE
cat("RMSE for Weekly GGM Model Predictions:", rmse_ggm_w, "\n")
RMSE for Weekly GGM Model Predictions: 3488834
# Daily GGM
# Scaling the sales data
sales_min <- min(sales_d_ts)
sales_max <- max(sales_d_ts)
sales_scaled <- (sales_d_ts - sales_min) / (sales_max - sales_min)
# View scaled data
summary(sales_scaled)
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.0000 0.1911 0.2868 0.3219 0.4343 1.0000
plot(sales_scaled, type = "l", main = "Scaled Daily Sales", xlab = "Day", ylab = "Scaled Sales")
We re-scale the data because else the model won’t converge
# Fit GGM models using scaled data
ggm1_d <- GGM(sales_scaled, mt = 'base', display = T)
Warning: NaNs producedWarning: NaNs producedWarning: NaNs produced
ggm2_d <- GGM(sales_scaled, mt = function(x) pchisq(x, 10), display = T)
ggm3_d <- GGM(sales_scaled, mt = function(x) log(x), display = T)
ggm4_d <- GGM(sales_scaled, mt = function(x) (x)^(1/1.05), display = T)
# Summarize models
summary(ggm1_d) # Base model
Call: ( Guseo Guidolin Model )
GGM(series = sales_scaled, mt = "base", display = T)
Residuals:
Min. 1st Qu. Median Mean 3rd Qu. Max.
-3.40209 -0.89405 0.18000 0.03836 0.97389 2.48042
Coefficients:
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error 1.199911 on 1034 degrees of freedom
Multiple R-squared: 0.999863 Residual sum of squares: 1488.74
summary(ggm2_d) # Chi-squared
Call: ( Guseo Guidolin Model )
GGM(series = sales_scaled, mt = function(x) pchisq(x, 10), display = T)
Residuals:
Min. 1st Qu. Median Mean 3rd Qu. Max.
-7.8716 -2.8996 -0.9350 -0.6934 1.6547 7.6841
Coefficients:
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error 3.370771 on 1036 degrees of freedom
Multiple R-squared: 0.998915 Residual sum of squares: 11771.13
summary(ggm3_d) # Log transformation
Call: ( Guseo Guidolin Model )
GGM(series = sales_scaled, mt = function(x) log(x), display = T)
Residuals:
Min. 1st Qu. Median Mean 3rd Qu. Max.
-6.0610 -2.1289 -0.4068 -0.4506 1.0511 5.8698
Coefficients:
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error 2.488528 on 1036 degrees of freedom
Multiple R-squared: 0.999409 Residual sum of squares: 6415.712
summary(ggm4_d) # Power transformation
Call: ( Guseo Guidolin Model )
GGM(series = sales_scaled, mt = function(x) (x)^(1/1.05), display = T)
Residuals:
Min. 1st Qu. Median Mean 3rd Qu. Max.
-3.33604 -0.98757 0.18545 0.07343 0.93872 3.00560
Coefficients:
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error 1.301786 on 1036 degrees of freedom
Multiple R-squared: 0.999838 Residual sum of squares: 1755.654
Predict on the best model based on fit and p-values We select model 1
# Prediction using GGM model
pred_ggm_d <- predict(ggm1_d, newx = c(1:length(sales_scaled)))
pred_ggm_d <- ts(pred_ggm_d, start = start(sales_scaled), frequency = frequency(sales_scaled))
pred.inst_ggm_d <- make.instantaneous(pred_ggm_d)
pred.inst_ggm_d <- ts(pred.inst_ggm_d, start = start(sales_scaled), frequency = frequency(sales_scaled))
# Re-scale predictions back to the original scale
pred_original_scale <- (pred.inst_ggm_d * (sales_max - sales_min)) + sales_min
# Plot actual vs fitted sales (original scale)
plot(sales_d_ts, type = "p", col = "black", pch = 16, cex = 0.7,
xlab = "Day", ylab = "Daily Sales", main = "Actual vs Fitted Sales (Original Scale)")
lines(pred_original_scale, col = "red", lwd = 2)
legend("topleft", legend = c("Actual Values", "Fitted Values (GGM, Original Scale)"),
col = c("black", "red"), pch = c(16, NA), lty = c(NA, 1), lwd = c(NA, 2))
# Analysis of residuals
res_GGM_d <- sales_d_ts - pred_original_scale
tsdisplay(res_GGM_d, main = "Residuals of GGM Model")
Residuals dont look stationary
# Check for stationarity of residuals
adf_test_d <- adf.test(res_GGM_d)
Warning: p-value smaller than printed p-value
print(adf_test_d) # If p-value < alpha, series is stationary
Augmented Dickey-Fuller Test
data: res_GGM_d
Dickey-Fuller = -7.7728, Lag order = 10, p-value = 0.01
alternative hypothesis: stationary
# according to this, they are stationary
# Check for autocorrelation in residuals
box_test_d <- Box.test(res_GGM_d, lag = 10, type = "Ljung-Box")
print(box_test_d) # If p-value > alpha, residuals are indep
Box-Ljung test
data: res_GGM_d
X-squared = 1405.1, df = 10, p-value < 2.2e-16
Residuals look stationary in the test but hey have serial correlation
# Calculate RMSE for GGM model predictions (original scale)
rmse_ggm_d <- calculate_rmse(observed = sales_d_ts, predicted = pred_original_scale)
# Print the RMSE
cat("RMSE for Daily GGM Model Predictions (Original Scale):", rmse_ggm_d, "\n")
RMSE for Daily GGM Model Predictions (Original Scale): 1600828
# adjust timeseries to ensure date consistency
sales_m_ts <- ts(sales_m_ts, frequency=12, start=c(2021, 11))
hw1_m<- hw(sales_m_ts, seasonal="additive")
hw2_m<- hw(sales_m_ts, seasonal="multiplicative")
# prediction
fitted_hw1 <- hw1_m$fitted
fitted_hw2 <- hw2_m$fitted
We now plot the models
# Create a data frame for ggplot
plot_data <- data.frame(
Time = time(sales_m_ts),
Actual = as.numeric(sales_m_ts),
Fitted_Additive = as.numeric(hw1_m$fitted),
Fitted_Multiplicative = as.numeric(hw2_m$fitted)
)
# Melt data for easier ggplot usage
library(reshape2)
plot_data_melted <- melt(plot_data, id.vars = "Time",
variable.name = "Series",
value.name = "Value")
# Plot using ggplot2
ggplot(plot_data_melted, aes(x = Time, y = Value, color = Series)) +
geom_point(data = subset(plot_data_melted, Series == "Actual"), size = 2) + # Actual values as dots
geom_line(data = subset(plot_data_melted, Series != "Actual"), size = 1) + # Fitted values as lines
labs(
title = "Actual vs Fitted Values",
x = "Time",
y = "Value",
color = "Series"
) +
scale_color_manual(
values = c("Actual" = "black", "Fitted_Additive" = "blue", "Fitted_Multiplicative" = "red"),
labels = c("Actual", "Fitted (Additive)", "Fitted (Multiplicative)")
) +
theme_minimal() +
theme(
legend.position = "top",
legend.title = element_text(face = "bold")
)
Looks like the multiplicative models follows the data more more closely in general.
# residuals
residuals_hw1 <- residuals(hw1_m)
residuals_hw2 <- residuals(hw2_m)
tsdisplay(residuals_hw1)
tsdisplay(residuals_hw2)
# Stationarity and Correlation
# check for stationarity of residuals
# additive
adf_test <- adf.test(residuals_hw1) # H0: series is non-stationary
print(adf_test) # if p-val < alpha, series not stationary
Augmented Dickey-Fuller Test
data: residuals_hw1
Dickey-Fuller = -1.8495, Lag order = 3, p-value = 0.6317
alternative hypothesis: stationary
# so with this model we achieve stationary series
# multiplicative
adf_test <- adf.test(residuals_hw2) # H0: series is non-stationary
print(adf_test) # if p-val < alpha, series not stationary
Augmented Dickey-Fuller Test
data: residuals_hw2
Dickey-Fuller = -2.0941, Lag order = 3, p-value = 0.5365
alternative hypothesis: stationary
# so with this model we achieve stationary series
# additive
# check for autocorrelation in residuals
Box.test(residuals_hw1, lag = 10, type = "Ljung-Box") # h0 res indep
Box-Ljung test
data: residuals_hw1
X-squared = 4.8498, df = 10, p-value = 0.901
# p-val > alpha => Dont reject h0, so residuals are indep
# additive
# check for autocorrelation in residuals
Box.test(residuals_hw2, lag = 10, type = "Ljung-Box") # h0 res indep
Box-Ljung test
data: residuals_hw2
X-squared = 10.493, df = 10, p-value = 0.3983
# p-val > alpha => Dont reject h0, so residuals are indep
Multiplicative model follows the data better and has slightly better residuals
# forecast
# save the forecast of the second model
forecast_hw1 <- forecast(hw1_m, h=12)
forecast_hw2 <- forecast(hw2_m, h=12)
# Forecast plot
# Plot the time series with both forecasts
autoplot(sales_m_ts) +
autolayer(forecast_hw1$mean, series="Additive Holt-Winters Forecast", PI=F) +
autolayer(forecast_hw2$mean, series="Multiplicative Holt-Winters Forecast", PI=F) +
ggtitle("Sales Forecast with Holt-Winters Models") +
xlab("Time") +
ylab("Sales") +
scale_color_manual(
values=c("Additive Holt-Winters Forecast" = "blue",
"Multiplicative Holt-Winters Forecast" = "red")
) +
theme_minimal() +
theme(legend.position = "top", legend.title = element_blank())
Warning: Ignoring unknown parameters: `PI`Warning: Ignoring unknown parameters: `PI`
# RMSE Calculation for Holt-Winters models
rmse_hw1 <- calculate_rmse(observed = sales_m_ts, predicted = fitted_hw1)
rmse_hw2 <- calculate_rmse(observed = sales_m_ts, predicted = fitted_hw2)
# Print RMSE values
cat("RMSE for Additive Holt-Winters Model:", rmse_hw1, "\n")
RMSE for Additive Holt-Winters Model: 14123520
cat("RMSE for Multiplicative Holt-Winters Model:", rmse_hw2, "\n")
RMSE for Multiplicative Holt-Winters Model: 13169921
Multiplicative model is better
The Holt winters model has a frequency limit of 24, so we cannot do larger than that. Weekly and daily data have 52 and 365 frequencies respectively so we cannot fit the model with the R implementation so far.
ARIMA is a acronym for Auto Regressive Integrated Moving Average, ARIMA (p,d,q) where p refers to the AR part, q refers to the MA part and d is the degree of first difference involved.
First we nwwd to check if the series is stationary
# see if series is stationary
adf.test(sales_m_ts) #H0, series is non-stationary
# p-val > 0.05 => dont reject, non stationary: series is not stationary
adf.test(diff(sales_m_ts)) #H0, series is non-stationary
# see the acf and pacf
tsdisplay(diff(sales_m_ts))
plot(sales_m_ts)
ndiffs(sales_m_ts)
[1] 1
tsdisplay(diff(sales_m_ts))
Correlogram plot maybe suggests AR-1 or MA-1 after first difference
# ARIMA(p,d,q) = (1,1,0)
arima1_m<- Arima(sales_m_ts, order=c(1,1,0))
summary(arima1_m)
Series: sales_m_ts
ARIMA(1,1,0)
Coefficients:
ar1
-0.3178
s.e. 0.1783
sigma^2 = 2.666e+14: log likelihood = -630.5
AIC=1265 AICc=1265.38 BIC=1268.11
Training set error measures:
ME RMSE MAE MPE MAPE
Training set 4664178 15867282 12399192 6.652001 14.52265
MASE ACF1
Training set 0.3786368 -0.07165611
# study residual to see if is a good model
resid1_m<- residuals(arima1_m)
tsdisplay(resid1_m)
Residuals look stationary after fitting ARIMA
auto_arima_m <- auto.arima(sales_m_ts)
auto_arima_m
Series: sales_m_ts
ARIMA(0,1,1) with drift
Coefficients:
ma1 drift
-0.3741 3475637
s.e. 0.1604 1659940
sigma^2 = 2.494e+14: log likelihood = -628.83
AIC=1263.66 AICc=1264.44 BIC=1268.33
autoplot(forecast(auto_arima_m))
checkresiduals(auto_arima_m)
Ljung-Box test
data: Residuals from ARIMA(0,1,1) with drift
Q* = 0.42136, df = 6, p-value = 0.9987
Model df: 1. Total lags used: 7
The residuals of the Autoarima look stationary
AIC of the the manual arima is 1265, while the one of the autoarima is 1263. Lets use the autoarima
# Fitted values from both models
fitted_auto_arima <- fitted(auto_arima_m)
fitted_arima1 <- fitted(arima1_m)
# Create a data frame for plotting
plot_data <- data.frame(
Time = time(sales_m_ts),
Actual = as.numeric(sales_m_ts),
Fitted_Auto_ARIMA = as.numeric(fitted_auto_arima),
Fitted_ARIMA1 = as.numeric(fitted_arima1)
)
# Melt the data frame
plot_data_melted <- melt(plot_data, id.vars = "Time",
variable.name = "Series",
value.name = "Value")
# Plot
ggplot(plot_data_melted, aes(x = Time, y = Value, color = Series)) +
geom_point(data = subset(plot_data_melted, Series == "Actual"), size = 2) + # Actual values as points
geom_line(data = subset(plot_data_melted, Series != "Actual"), size = 1) + # Fitted values as lines
labs(
title = "Actual vs Fitted Values for ARIMA Models",
x = "Time",
y = "Sales",
color = "Series"
) +
scale_color_manual(
values = c("Actual" = "black", "Fitted_Auto_ARIMA" = "blue", "Fitted_ARIMA1" = "red"),
labels = c("Actual", "Fitted (Auto ARIMA)", "Fitted (ARIMA(1,1,0))")
) +
theme_minimal() +
theme(
legend.position = "top",
legend.title = element_blank()
)
NA
NA
# Calculate RMSE for the fitted values
# Calculate RMSE for each model
rmse_auto_arima <- calculate_rmse(observed = sales_m_ts, predicted = fitted_auto_arima)
rmse_arima1 <- calculate_rmse(observed = sales_m_ts, predicted = fitted_arima1)
# Print RMSE values
cat("RMSE for Auto ARIMA Model:", rmse_auto_arima, "\n")
RMSE for Auto ARIMA Model: 15118942
cat("RMSE for ARIMA(1,1,0) Model:", rmse_arima1, "\n")
RMSE for ARIMA(1,1,0) Model: 15867282
The RMSE of the Autoarima is better as is the AIC.
The ARIMA(0,1,1) model can be described simply as a random walk with drift. Here’s what that means:
AR (AutoRegressive) Part:
I (Integrated) Part:
MA (Moving Average) Part:
An ARIMA(0,1,1) model is suitable when:
The d=1 parameter in ARIMA(0,1,1) indicates that the series is differenced once to achieve stationarity. Before differencing, the series may exhibit a linear trend or random walk behavior. After differencing, the series should show no trend and have relatively stable mean and variance
The q=1 in ARIMA(0,1,1) indicates that the series is modeled with a first-order moving average component after differencing. The autocorrelation function (ACF) of the differenced series should show: A significant spike at lag 1. Rapid decay to zero after lag 1. The partial autocorrelation function (PACF) should show no significant lags.
# study residual to see if is a good model
resid_autoarima_m<- residuals(auto_arima_m)
tsdisplay(resid_autoarima_m)
# see if series is stationary
adf.test(sales_w_ts) #H0, series is non-stationary
Augmented Dickey-Fuller Test
data: sales_w_ts
Dickey-Fuller = -2.9189, Lag order = 5, p-value = 0.1934
alternative hypothesis: stationary
# p-val > 0.05 => dont reject, non stationary: series is not stationary
adf.test(diff(sales_w_ts)) # after diff is sationary
Warning: p-value smaller than printed p-value
Augmented Dickey-Fuller Test
data: diff(sales_w_ts)
Dickey-Fuller = -6.5436, Lag order = 5, p-value = 0.01
alternative hypothesis: stationary
After differencing, looks stationary
tsdisplay(diff(sales_w_ts))
Correlograms suggest maybe AR 1 or MA 1.
### Manual ARIMA------------
# ARIMA(p,d,q) = (1,1,0)
arima1_w<- Arima(sales_w_ts, order=c(1,1,0))
summary(arima1_w)
Series: sales_w_ts
ARIMA(1,1,0)
Coefficients:
ar1
-0.4400
s.e. 0.0749
sigma^2 = 1.17e+13: log likelihood = -2502.2
AIC=5008.4 AICc=5008.48 BIC=5014.45
Training set error measures:
ME RMSE MAE MPE MAPE
Training set 159889.8 3398717 2549146 -0.9012317 12.90507
MASE ACF1
Training set 0.3542043 -0.04856579
auto_arima_w <- auto.arima(sales_w_ts)
summary(auto_arima_w)
Series: sales_w_ts
ARIMA(0,1,1)
Coefficients:
ma1
-0.5454
s.e. 0.0763
sigma^2 = 1.13e+13: log likelihood = -2499.58
AIC=5003.15 AICc=5003.23 BIC=5009.2
Training set error measures:
ME RMSE MAE MPE MAPE
Training set 294210.8 3339058 2474168 -0.2764229 12.33848
MASE ACF1
Training set 0.3437861 -0.008618996
AIC on the Autoarima is better, lets go with that one
checkresiduals(auto_arima_w)
Ljung-Box test
data: Residuals from ARIMA(0,1,1)
Q* = 18.205, df = 30, p-value = 0.9551
Model df: 1. Total lags used: 31
Residuals look stationary, see the plots for both models
# Fit ARIMA models for weekly data
arima1_w <- Arima(sales_w_ts, order = c(1, 1, 0))
auto_arima_w <- auto.arima(sales_w_ts)
# Extract fitted values for both models
fitted_arima1_w <- fitted(arima1_w)
fitted_auto_arima_w <- fitted(auto_arima_w)
# Create a data frame for plotting
plot_data <- data.frame(
Time = time(sales_w_ts),
Actual = as.numeric(sales_w_ts),
Fitted_ARIMA1 = as.numeric(fitted_arima1_w),
Fitted_Auto_ARIMA = as.numeric(fitted_auto_arima_w)
)
# Melt the data frame for ggplot2
plot_data_melted <- melt(plot_data, id.vars = "Time",
variable.name = "Series",
value.name = "Value")
# Plot using ggplot2
ggplot(plot_data_melted, aes(x = Time, y = Value, color = Series)) +
geom_point(data = subset(plot_data_melted, Series == "Actual"), size = 2) + # Actual values as points
geom_line(data = subset(plot_data_melted, Series != "Actual"), size = 1) + # Fitted values as lines
labs(
title = "Actual vs Fitted Values for ARIMA Models (Weekly)",
x = "Time",
y = "Sales",
color = "Series"
) +
scale_color_manual(
values = c("Actual" = "black", "Fitted_ARIMA1" = "red", "Fitted_Auto_ARIMA" = "blue"),
labels = c("Actual", "Fitted (ARIMA(1,1,0))", "Fitted (Auto ARIMA)")
) +
theme_minimal() +
theme(
legend.position = "top",
legend.title = element_blank()
)
# Calculate RMSE for both models
rmse_arima1_w <- calculate_rmse(observed = sales_w_ts, predicted = fitted_arima1_w)
rmse_auto_arima_w <- calculate_rmse(observed = sales_w_ts, predicted = fitted_auto_arima_w)
# Print RMSE values
cat("RMSE for ARIMA(1,1,0) Model (Weekly):", rmse_arima1_w, "\n")
RMSE for ARIMA(1,1,0) Model (Weekly): 3398717
cat("RMSE for Auto ARIMA Model (Weekly):", rmse_auto_arima_w, "\n")
RMSE for Auto ARIMA Model (Weekly): 3339058
The Auto-arima is also better in terms of RMSE
# see if series is stationary
adf.test(sales_d_ts) #H0, series is non-stationary
# p-val < 0.05 => reject non stationary: series might be stationary
No need for differencing because is already stationary, try to model with arima
tsdisplay(sales_d_ts)
Autocorrelograms are not easy to interpret, but lets try with a baseline model
# ARIMA(p,d,q) = (2,1,0)
arima1_d<- Arima(sales_d_ts, order=c(1,0,1))
summary(arima1_d)
checkresiduals(arima1_d)
Residuals look not entirely stationary
Try to model with automatic approach:
auto_arima_d <- auto.arima(sales_d_ts)
summary(auto_arima_d)
checkresiduals(auto_arima_d)
Rresiduals improve, and AIC is lower in the autoarima Check the fit for both models
# Extract fitted values for both models
fitted_arima1_d <- fitted(arima1_d)
fitted_auto_arima_d <- fitted(auto_arima_d)
# Create a data frame for plotting
plot_data <- data.frame(
Time = time(sales_d_ts),
Actual = as.numeric(sales_d_ts),
Fitted_ARIMA1 = as.numeric(fitted_arima1_d),
Fitted_Auto_ARIMA = as.numeric(fitted_auto_arima_d)
)
# Melt the data frame for ggplot2
plot_data_melted <- melt(plot_data, id.vars = "Time",
variable.name = "Series",
value.name = "Value")
# Plot using ggplot2
ggplot(plot_data_melted, aes(x = Time, y = Value, color = Series)) +
geom_point(data = subset(plot_data_melted, Series == "Actual"), size = 2) + # Actual values as points
geom_line(data = subset(plot_data_melted, Series != "Actual"), size = 1) + # Fitted values as lines
labs(
title = "Actual vs Fitted Values for ARIMA Models (Daily)",
x = "Time",
y = "Sales",
color = "Series"
) +
scale_color_manual(
values = c("Actual" = "black", "Fitted_ARIMA1" = "red", "Fitted_Auto_ARIMA" = "blue"),
labels = c("Actual", "Fitted (ARIMA(1,0,1))", "Fitted (Auto ARIMA)")
) +
theme_minimal() +
theme(
legend.position = "top",
legend.title = element_blank()
)
Plot is not readable, but check the RMSE for both models to confirm wihch fits better
# Calculate RMSE for both models
rmse_arima1_d <- calculate_rmse(observed = sales_d_ts, predicted = fitted_arima1_d)
rmse_auto_arima_d <- calculate_rmse(observed = sales_d_ts, predicted = fitted_auto_arima_d)
# Print RMSE values
cat("RMSE for ARIMA(1,0,1) Model (Daily):", rmse_arima1_d, "\n")
cat("RMSE for Auto ARIMA Model (Daily):", rmse_auto_arima_d, "\n")
Autoarima is much better, now try to improve with seasonality, beacuse daily data looks seasonal each 7 days.
# Daily sales
tsdisplay(sales_d_ts) #
tsdisplay(diff(sales_d_ts))
sarima_d <- auto.arima(sales_d_ts, seasonal=TRUE)
summary(sarima_d)
resid_ds<- residuals(sarima_d)
tsdisplay(resid_ds)
# check for autocorrelation
Box.test(residuals(sarima_d), type="Ljung-Box")
# A low p-value (<0.05) suggests residual autocorrelation.
Looks like Aarima is the same in terms of AIC, lets check the RMSE:
# Extract fitted values for both models
fitted_sarima_d <- fitted(sarima_d)
# Calculate RMSE for both models
rmse_sarima_d <- calculate_rmse(observed = sales_d_ts, predicted = fitted_sarima_d)
# Print RMSE values
cat("RMSE for Auto ARIMA Model (Daily):", rmse_auto_arima_d, "\n")
cat("RMSE for Seasonal ARIMA Model (Daily):", rmse_sarima_d, "\n")
The RMSE is exactly the same, they are the same model.
Refine SARIMA with external regressors
# readefine sales_d_ts
head(df_merged_d)
sales_d_ts <- ts(exp(df_merged_d$sales_cop), frequency=365, start=c(2021, 334)) # 334 is November 30
seasonal_sales_d_ts <- ts(exp(df_merged_d$sales_cop), frequency=7, start=c(2021, 334)) # 334 is November 30
plot(sales_d_ts)
tsdisplay(sales_d_ts,lag.max = 30)
tsdisplay(seasonal_sales_d_ts,lag.max = 30)
# define regresors
# Select specific columns by name
x_regressors_d <- df_merged_d %>% select(rain_sum, fx, tmedian)
# Apply the exponential function to each column
x_regressors_d <- as.data.frame(apply(x_regressors_d, 2, exp))
# Convert to a matrix for ARIMA modeling
x_regressors_d <- as.matrix(x_regressors_d)
# fit the model on sales
# Fit an auto.arima model with seasonal component and external regressors
sarimax_model_d <- auto.arima(
sales_d_ts,
seasonal = TRUE, # Enable seasonal components
xreg = x_regressors_d # External regressors
)
# Display the summary of the fitted model
summary(sarimax_model_d)
The AIC actually decreases, lets check the RMSE
# Extract fitted values for all models
fitted_sarimax_d <- fitted(sarimax_model_d)
# Calculate RMSE for all models
rmse_sarimax_d <- calculate_rmse(observed = sales_d_ts, predicted = fitted_sarimax_d)
# Print RMSE values
cat("RMSE for Auto ARIMA Model (Daily):", rmse_auto_arima_d, "\n")
cat("RMSE for Seasonal ARIMA Model (Daily):", rmse_sarima_d, "\n")
cat("RMSE for SARIMAX Model (Daily):", rmse_sarimax_d, "\n")
The RMSE also worsens, so stay with regular Auto-ARIMA
Monthly Sales
fit_m1 <- ses(sales_m_ts, alpha = 0.2, initial = 'simple', h=5)
fit_m2 <- ses(sales_m_ts, alpha = 0.6, initial = 'simple', h=5)
fit_m3 <- ses(sales_m_ts, h=5)
plot(sales_m_ts, ylab='Monthly Sales', xlab='Months')
lines(fitted(fit_m1), col='blue', type='o')
lines(fitted(fit_m2), col='red', type='o')
lines(fitted(fit_m3), col='green', type='o')
forecast_m1 <- ses(sales_m_ts, h=5)
# Accuracy of one-step-ahead training errors
round(accuracy(forecast_m1),2)
ME RMSE MAE MPE MAPE MASE ACF1
Training set 3207582 17626876 13250973 -12.1 29.7 0.4 -0.05
summary(forecast_m1)
Forecast method: Simple exponential smoothing
Model Information:
Simple exponential smoothing
Call:
ses(y = sales_m_ts, h = 5)
Smoothing parameters:
alpha = 0.675
Initial states:
l = 56978123.3871
sigma: 18137906
AIC AICc BIC
1336.322 1337.072 1341.073
Error measures:
ME RMSE MAE MPE MAPE
Training set 3207582 17626876 13250973 -12.09656 29.70395
MASE ACF1
Training set 0.4046478 -0.0504105
Forecasts:
autoplot(forecast_m1) + autolayer(fitted(forecast_m1),series='Fitted') + ylab("Monthly Sales")+xlab("Months")
# Extract fitted values for each model
fitted_m1 <- fitted(fit_m1)
fitted_m2 <- fitted(fit_m2)
fitted_m3 <- fitted(fit_m3)
# Calculate RMSE for each model
rmse_m1 <- calculate_rmse(observed = sales_m_ts, predicted = fitted_m1)
rmse_m2 <- calculate_rmse(observed = sales_m_ts, predicted = fitted_m2)
rmse_m3 <- calculate_rmse(observed = sales_m_ts, predicted = fitted_m3)
# Print RMSE values
cat("RMSE for SES Model 1 (alpha = 0.2):", rmse_m1, "\n")
RMSE for SES Model 1 (alpha = 0.2): 23924620
cat("RMSE for SES Model 2 (alpha = 0.6):", rmse_m2, "\n")
RMSE for SES Model 2 (alpha = 0.6): 16189623
cat("RMSE for SES Model 3 (Optimized alpha):", rmse_m3, "\n")
RMSE for SES Model 3 (Optimized alpha): 17626876
rmse_exp_sm_m <- rmse_m2
Weekly Sales
For weekly data, exponential smoothing can capture longer-term trends and seasonal patterns that repeat on a weekly basis. Weekly data can also have seasonal components related to months, quarters, or years.
fit_w1 <- ses(sales_w_ts, alpha = 0.2, initial = 'simple', h=5)
fit_w2 <- ses(sales_w_ts, alpha = 0.6, initial = 'simple', h=5)
fit_w3 <- ses(sales_w_ts, h=5)
plot(sales_w_ts, ylab='Weekly Sales', xlab='Weeks')
lines(fitted(fit_w1), col='blue', type='o')
lines(fitted(fit_w2), col='red', type='o')
lines(fitted(fit_w3), col='green', type='o')
forecast_w1 <- ses(sales_w_ts, h=5)
round(accuracy(forecast_w1),2)
ME RMSE MAE MPE MAPE MASE ACF1
Training set 287718.1 3340420 2478696 -0.46 12.47 0.34 0
summary(forecast_w1)
Forecast method: Simple exponential smoothing
Model Information:
Simple exponential smoothing
Call:
ses(y = sales_w_ts, h = 5)
Smoothing parameters:
alpha = 0.4505
Initial states:
l = 6860998.2575
sigma: 3362470
AIC AICc BIC
5372.269 5372.430 5381.360
Error measures:
ME RMSE MAE MPE MAPE
Training set 287718.1 3340420 2478696 -0.4614222 12.4674
MASE ACF1
Training set 0.3444153 -0.004238849
Forecasts:
autoplot(forecast_w1) + autolayer(fitted(forecast_w1),series='Fitted') + ylab("Weekly Sales")+xlab("Weeks")
# Extract fitted values for each model
fitted_w1 <- fitted(fit_w1)
fitted_w2 <- fitted(fit_w2)
fitted_w3 <- fitted(fit_w3)
# Calculate RMSE for each model
rmse_w1 <- calculate_rmse(observed = sales_w_ts, predicted = fitted_w1)
rmse_w2 <- calculate_rmse(observed = sales_w_ts, predicted = fitted_w2)
rmse_w3 <- calculate_rmse(observed = sales_w_ts, predicted = fitted_w3)
# Print RMSE values
cat("RMSE for SES Model 1 (alpha = 0.2):", rmse_w1, "\n")
RMSE for SES Model 1 (alpha = 0.2): 3548490
cat("RMSE for SES Model 2 (alpha = 0.6):", rmse_w2, "\n")
RMSE for SES Model 2 (alpha = 0.6): 3375868
cat("RMSE for SES Model 3 (Optimized alpha):", rmse_w3, "\n")
RMSE for SES Model 3 (Optimized alpha): 3340420
rmse_exp_sm_w <- rmse_w3
Daily Sales
For daily data, exponential smoothing can be used to forecast short-term trends and seasonal patterns. When applying exponential smoothing to daily data, you need to consider:
Seasonality: Daily data often exhibit seasonal patterns, such as weekly cycles (e.g., higher sales on weekends).
Holidays and special events: These can cause irregular patterns in daily data that may need to be accounted for.
fit_d1 <- ses(sales_d_ts, alpha = 0.2, initial = 'simple', h=5)
fit_d2 <- ses(sales_d_ts, alpha = 0.6, initial = 'simple', h=5)
fit_d3 <- ses(sales_d_ts, h=5)
plot(sales_d_ts, ylab='Daily Sales', xlab='Days')
lines(fitted(fit_d1), col='blue', type='o')
lines(fitted(fit_d2), col='red', type='o')
lines(fitted(fit_d3), col='green', type='o')
forecast_d1 <- ses(sales_d_ts, h=5)
round(accuracy(forecast_d1),2)
ME RMSE MAE MPE MAPE MASE ACF1
Training set 86503.09 1609483 1258308 -67.1 93.29 0.55 0.4
summary(forecast_d1)
Forecast method: Simple exponential smoothing
Model Information:
Simple exponential smoothing
Call:
ses(y = sales_d_ts, h = 5)
Smoothing parameters:
alpha = 0.0393
Initial states:
l = 878511.458
sigma: 1611034
AIC AICc BIC
36920.49 36920.51 36935.32
Error measures:
ME RMSE MAE MPE MAPE
Training set 86503.09 1609483 1258308 -67.10294 93.28754
MASE ACF1
Training set 0.5505054 0.3989636
Forecasts:
autoplot(forecast_d1) + autolayer(fitted(forecast_d1),series='Fitted') + ylab("Daily Sales")+xlab("Days")
# Extract fitted values for each model
fitted_d1 <- fitted(fit_d1)
fitted_d2 <- fitted(fit_d2)
fitted_d3 <- fitted(fit_d3)
# Calculate RMSE for each model
rmse_d1 <- calculate_rmse(observed = sales_d_ts, predicted = fitted_d1)
rmse_d2 <- calculate_rmse(observed = sales_d_ts, predicted = fitted_d2)
rmse_d3 <- calculate_rmse(observed = sales_d_ts, predicted = fitted_d3)
# Print RMSE values
cat("RMSE for SES Model 1 (alpha = 0.2):", rmse_d1, "\n")
RMSE for SES Model 1 (alpha = 0.2): 1676166
cat("RMSE for SES Model 2 (alpha = 0.6):", rmse_d2, "\n")
RMSE for SES Model 2 (alpha = 0.6): 1752876
cat("RMSE for SES Model 3 (Optimized alpha):", rmse_d3, "\n")
RMSE for SES Model 3 (Optimized alpha): 1609483
rmse_exp_sm_d <- rmse_d3
# GGM part
# Summary of the GGM model
summary(ggm1) # Assume ggm1_m is the monthly GGM model
Call: ( Guseo Guidolin Model )
GGM(series = sales_m_ts, mt = "base", display = T)
Residuals:
Min. 1st Qu. Median Mean 3rd Qu. Max.
-27544719 -8809035 742251 -337148 7701034 23238738
Coefficients:
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error 13318300 on 31 degrees of freedom
Multiple R-squared: 0.999873 Residual sum of squares: 5.498691e+15
# Predictions using GGM
pred_GGM_m <- predict(ggm1, newx = matrix(1:length(sales_m_ts), ncol = 1))
pred_GGM_m.inst <- make.instantaneous(pred_GGM_m)
# Convert predictions to a time series
start_time_m <- start(sales_m_ts) # Start time from sales_m_ts
frequency_m <- frequency(sales_m_ts) # Frequency from sales_m_ts
pred_GGM_m_vec <- unlist(pred_GGM_m.inst) # Convert predictions to a numeric vector
pred_GGM_m_ts <- ts(pred_GGM_m_vec, start = start_time_m, frequency = frequency_m)
# Plot actual vs GGM predictions
plot(sales_m_ts, type = "b", xlab = "Month", ylab = "Monthly Sales", pch = 16, lty = 3, cex = 0.6)
lines(pred_GGM_m_ts, col = "red", lty = 2)
#### SARIMAX Refinement------------------------
# Get fitted values from the GGM model
fit.sales_m <- fitted(ggm1)
# Check length consistency
if (length(fit.sales_m) != length(sales_m_ts)) {
stop("fit.sales_m and sales_m_ts lengths do not match")
}
# Scale GGM fitted values and the cumulative sales
fit.sales_m <- scale(fit.sales_m)
sales_m_ts_scaled <- scale(cumsum(sales_m_ts)) # Scale the cumulative sales for convergence
# Fit SARIMAX with GGM fitted values as regressors
sarima_m <- Arima(
sales_m_ts_scaled,
order = c(1, 0, 1),
seasonal = list(order = c(0, 0, 1), period = 12), # Monthly seasonality
xreg = fit.sales_m
)
summary(sarima_m)
Series: sales_m_ts_scaled
Regression with ARIMA(1,0,1)(0,0,1)[12] errors
Coefficients:
ar1 ma1 sma1 intercept xreg
0.3609 0.2995 -0.1012 0.0002 1.0007
s.e. 0.2233 0.2162 0.1925 0.0028 0.0029
sigma^2 = 9.454e-05: log likelihood = 118.13
AIC=-224.25 AICc=-221.36 BIC=-214.75
Training set error measures:
ME RMSE MAE MPE
Training set 6.956468e-05 0.009022524 0.006945702 -2.619138
MAPE MASE ACF1
Training set 4.22122 0.07700823 0.04863719
# Reverse scaling for fitted cumulative values
fitted_cumulative <- fitted(sarima_m)
scaling_center <- attr(sales_m_ts_scaled, "scaled:center")
scaling_scale <- attr(sales_m_ts_scaled, "scaled:scale")
fitted_cumulative_original <- fitted_cumulative * scaling_scale + scaling_center
# Convert cumulative fitted values to instantaneous values
fitted_instantaneous <- diff(c(fitted_cumulative_original, NA)) # Add NA to align lengths
# Create a time series object for the fitted instantaneous values
fitted_instantaneous_ts <- ts(
fitted_instantaneous,
start = start(sales_m_ts),
frequency = frequency(sales_m_ts)
)
# Plot actual vs fitted instantaneous values
plot(sales_m_ts, type = "p", col = "blue", pch = 16,
main = "Original vs Fitted Instantaneous Values (Monthly)",
xlab = "Time", ylab = "Instantaneous Values")
lines(fitted_instantaneous_ts, col = "red", lwd = 3, lty = 1)
# Add legend
legend("bottomright", legend = c("Original sales", "Fitted sales"),
col = c("blue", "red"), lty = c(NA, 1), pch = c(16, NA), lwd = c(NA, 3))
# Calculate RMSE for fitted_instantaneous_ts against sales_m_ts
rmse_mixture_m <- calculate_rmse(observed = sales_m_ts, predicted = fitted_instantaneous_ts)
# Print the RMSE value
cat("RMSE for Fitted Instantaneous Values (GGM + SARIMAX):", rmse_mixture_m, "\n")
RMSE for Fitted Instantaneous Values (GGM + SARIMAX): 6978426
resid_mixture_m <- sales_m_ts - fitted_instantaneous_ts
tsdisplay(resid_mixture_m)
Residuals have autocorrelation at lag 1
#### GGM-------------------------------
summary(ggm1_w) # this one is best model found
Call: ( Guseo Guidolin Model )
GGM(series = sales_w_ts, mt = "base", display = T)
Residuals:
Min. 1st Qu. Median Mean 3rd Qu. Max.
-31498207 -8733958 2309014 276818 8889298 21142720
Coefficients:
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error 12329105 on 148 degrees of freedom
Multiple R-squared: 0.999873 Residual sum of squares: 2.249701e+16
pred_GGM_w<- predict(ggm1_w, newx=matrix(1:length(sales_w_ts), ncol=1))
pred_GGM_w.inst<- make.instantaneous(pred_GGM_w)
# set same timeframe for GGM preds
start_time_w <- start(sales_w_ts) # Get start time from sales_w_ts
frequency_w <- frequency(sales_w_ts) # Get frequency from sales_w_ts
# Convert pred_GGM to a numeric vector
pred_GGM_w_vec <- unlist(pred_GGM_w.inst) # Flatten the list to a numeric vector
# Create the time series for pred_GGM
pred_GGM_w_ts <- ts(pred_GGM_w_vec, start = start_time_w, frequency = frequency_w)
plot(sales_w_ts, type= "b",xlab="Week", ylab="Weekly Sales", pch=16, lty=3, cex=0.6)
lines(pred_GGM_w_ts, col = "red", lty = 2)
NA
NA
# SARMAX refinement
fit.sales_w <- fitted(ggm1_w) # Predicted values from the GGM model
if (length(fit.sales_w) != length(sales_w_ts)) {
stop("fit.sales_w and sales_w_ts lengths do not match")
}
fit.sales_w <- scale(fit.sales_w) # scale regresor to make convergence
sales_w_ts_scaled <- scale(cumsum(sales_w_ts)) # Scale the time series because if not will not reach convergence
sarima_w <- Arima(
sales_w_ts_scaled,
order = c(1, 0, 1),
seasonal = list(order = c(0, 0, 1), period = 52),
xreg = fit.sales_w # this is the GGM fitted values
)
summary(sarima_w)
Series: sales_w_ts_scaled
Regression with ARIMA(1,0,1)(0,0,1)[52] errors
Coefficients:
ar1 ma1 sma1 intercept xreg
0.9351 0.2911 -0.0164 0.0003 0.9995
s.e. 0.0269 0.0625 0.1091 0.0044 0.0038
sigma^2 = 9.19e-06: log likelihood = 671.32
AIC=-1330.64 AICc=-1330.06 BIC=-1312.45
Training set error measures:
ME RMSE MAE MPE
Training set -2.379355e-05 0.002981512 0.002297777 -0.9188761
MAPE MASE ACF1
Training set 1.382329 0.1077522 0.1024892
# get fitted values
# Extract the fitted cumulative values from the SARIMA model
fitted_cumulative <- fitted(sarima_w)
# Reverse scaling transformation to get fitted cumulative values in the original scale
scaling_center <- attr(sales_w_ts_scaled, "scaled:center")
scaling_scale <- attr(sales_w_ts_scaled, "scaled:scale")
fitted_cumulative_original <- fitted_cumulative * scaling_scale + scaling_center
# Convert cumulative fitted values to instantaneous values
fitted_instantaneous <- diff(c(fitted_cumulative_original, NA)) # Add NA to align lengths
# Create a time series object for the fitted instantaneous values
fitted_instantaneous_ts <- ts(
fitted_instantaneous,
start = start(sales_w_ts),
frequency = frequency(sales_w_ts)
)
# Plot original instantaneous values vs fitted instantaneous values
plot(sales_w_ts, type = "p", col = "blue", pch = 16,
main = "Original vs Fitted Instantaneous Values",
xlab = "Time", ylab = "Instantaneous Values")
# Add the fitted instantaneous values as a line
lines(fitted_instantaneous_ts, col = "red", lwd = 3, lty = 1)
# Add legend
legend("bottomright", legend = c("Original Instantaneous", "Fitted Instantaneous"),
col = c("blue", "red"), lty = c(NA, 1), pch = c(16, NA), lwd = c(NA, 3))
# Residuals
# Step 1: Extract residuals from the SARIMA model
resid_w <- residuals(sarima_w)
# Step 2: Visualize residuals
# Time series plot of residuals
tsdisplay(resid_w, main = "Residual Diagnostics for SARIMA Model")
# Step 3: Test residuals for stationarity
adf_test <- adf.test(resid_w)
Warning: p-value smaller than printed p-value
cat("ADF Test p-value:", adf_test$p.value, "\n")
ADF Test p-value: 0.01
if (adf_test$p.value < 0.05) {
cat("The residuals are stationary.\n")
} else {
cat("The residuals are not stationary.\n")
}
The residuals are stationary.
# Step 4: Test residuals for white noise (no autocorrelation)
ljung_box_test <- Box.test(resid_w, lag = 20, type = "Ljung-Box")
cat("Ljung-Box Test p-value:", ljung_box_test$p.value, "\n")
Ljung-Box Test p-value: 1.110658e-05
if (ljung_box_test$p.value > 0.05) {
cat("The residuals resemble white noise (uncorrelated).\n")
} else {
cat("The residuals show significant autocorrelation.\n")
}
The residuals show significant autocorrelation.
Stationary residuals but with significant correlation
#### RMSE for SARIMAX Predictions ####
rmse_mixture_w <- calculate_rmse(observed = sales_w_ts, predicted = fitted_instantaneous_ts)
# Print RMSE for SARIMAX
cat("RMSE for SARIMAX Predictions:", rmse_mixture_w, "\n")
RMSE for SARIMAX Predictions: 1202671
# Scaling the sales data
sales_min <- min(sales_d_ts)
sales_max <- max(sales_d_ts)
sales_scaled <- (sales_d_ts - sales_min) / (sales_max - sales_min)
# View scaled data
summary(sales_scaled)
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.0000 0.1911 0.2868 0.3219 0.4343 1.0000
plot(sales_scaled, type = "l", main = "Scaled Daily Sales", xlab = "Day", ylab = "Scaled Sales")
#### GGM-------------------------------
# Fit GGM model using scaled data
ggm1_d <- GGM(sales_scaled, mt = 'base', display = T)
Warning: NaNs producedWarning: NaNs producedWarning: NaNs produced
summary(ggm1_d)
Call: ( Guseo Guidolin Model )
GGM(series = sales_scaled, mt = "base", display = T)
Residuals:
Min. 1st Qu. Median Mean 3rd Qu. Max.
-3.40209 -0.89405 0.18000 0.03836 0.97389 2.48042
Coefficients:
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error 1.199911 on 1034 degrees of freedom
Multiple R-squared: 0.999863 Residual sum of squares: 1488.74
# Predictions using GGM
pred_GGM_d <- predict(ggm1_d, newx = matrix(1:length(sales_scaled), ncol = 1))
pred_GGM_d.inst <- make.instantaneous(pred_GGM_d)
# Convert predictions to a time series
start_time_d <- start(sales_scaled) # Start time from scaled sales
frequency_d <- frequency(sales_scaled) # Frequency from scaled sales
pred_GGM_d_vec <- unlist(pred_GGM_d.inst) # Convert predictions to a numeric vector
pred_GGM_d_ts <- ts(pred_GGM_d_vec, start = start_time_d, frequency = frequency_d)
# Plot scaled GGM predictions
plot(sales_scaled, type = "b", xlab = "Day", ylab = "Scaled Daily Sales", pch = 16, lty = 3, cex = 0.6)
lines(pred_GGM_d_ts, col = "red", lty = 2)
#### SARIMAX Refinement------------------------
# Use instantaneous fitted values from the GGM model
fit.sales_d_instantaneous <- pred_GGM_d.inst
# Ensure lengths match
if (length(fit.sales_d_instantaneous) != length(sales_scaled)) {
stop("Instantaneous fitted values and scaled sales data lengths do not match!")
}
# Fit SARIMAX with instantaneous GGM fitted values as regressors
sarima_d <- auto.arima(
sales_scaled,
seasonal = TRUE, # Enable seasonal components
xreg = fit.sales_d_instantaneous, # Use instantaneous GGM values as regressors
stepwise = TRUE, # Enable stepwise selection (faster)
approximation = FALSE # Use exact maximum likelihood
)
summary(sarima_d)
Series: sales_scaled
Regression with ARIMA(2,0,2) errors
Coefficients:
ar1 ar2 ma1 ma2 xreg
1.2120 -0.9762 -1.0599 0.7847 1.0033
s.e. 0.0088 0.0082 0.0296 0.0233 0.0102
sigma^2 = 0.01321: log likelihood = 774.91
AIC=-1537.82 AICc=-1537.73 BIC=-1508.14
Training set error measures:
ME RMSE MAE MPE MAPE
Training set 2.328979e-07 0.114653 0.08637051 -Inf Inf
MASE ACF1
Training set 0.3897133 0.146021
# Extract fitted scaled values from the SARIMAX model
fitted_scaled <- fitted(sarima_d)
# Reverse scaling for final fitted instantaneous values
fitted_instantaneous_ts <- fitted_scaled * (sales_max - sales_min) + sales_min
# Reverse scaling for GGM predictions
pred_GGM_d_original <- pred_GGM_d_ts * (sales_max - sales_min) + sales_min
# Plot actual vs fitted instantaneous values
plot(sales_d_ts, type = "p", col = "blue", pch = 16,
main = "Original vs Fitted Instantaneous Values (Daily)",
xlab = "Time", ylab = "Instantaneous Values")
lines(fitted_instantaneous_ts, col = "red", lwd = 3, lty = 1)
# Add legend
legend("topright", legend = c("Original Instantaneous", "Fitted Instantaneous"),
col = c("blue", "red"), lty = c(NA, 1), pch = c(16, NA), lwd = c(NA, 3))
#### Residuals-----------------------
# Extract residuals from the SARIMA model
resid_d <- residuals(sarima_d)
# Visualize residuals
tsdisplay(resid_d, main = "Residual Diagnostics for SARIMA Model")
# Test residuals for stationarity
adf_test <- adf.test(resid_d)
Warning: p-value smaller than printed p-value
cat("ADF Test p-value:", adf_test$p.value, "\n")
ADF Test p-value: 0.01
if (adf_test$p.value < 0.05) {
cat("The residuals are stationary.\n")
} else {
cat("The residuals are not stationary.\n")
}
The residuals are stationary.
# Test residuals for white noise (no autocorrelation)
ljung_box_test <- Box.test(resid_d, lag = 20, type = "Ljung-Box")
cat("Ljung-Box Test p-value:", ljung_box_test$p.value, "\n")
Ljung-Box Test p-value: 0
if (ljung_box_test$p.value > 0.05) {
cat("The residuals resemble white noise (uncorrelated).\n")
} else {
cat("The residuals show significant autocorrelation.\n")
}
The residuals show significant autocorrelation.
#### RMSE for SARIMAX Predictions ####
rmse_mixture_d <- calculate_rmse(observed = sales_d_ts, predicted = fitted_instantaneous_ts)
# Print RMSE for SARIMAX
cat("RMSE for SARIMAX Predictions:", rmse_mixture_d, "\n")
RMSE for SARIMAX Predictions: 1182471
This model was introduced by Facebook (S. J. Taylor & Letham, 2018), originally for forecasting daily data with weekly and yearly seasonality, plus holiday effects. It was later extended to cover more types of seasonal data. It works best with time series that have strong seasonality and several seasons of historical data.
Prophet can be considered a nonlinear regression model (Chapter 7), of the form yt=g(t)+s(t)+h(t)+εt, where g(t) describes a piecewise-linear trend (or “growth term”), s(t) describes the various seasonal patterns, h(t) captures the holiday effects, and εt is a white noise error term.
The knots (or changepoints) for the piecewise-linear trend are automatically selected if not explicitly specified. Optionally, a logistic function can be used to set an upper bound on the trend.
The seasonal component consists of Fourier terms of the relevant periods. By default, order 10 is used for annual seasonality and order 3 is used for weekly seasonality.
Holiday effects are added as simple dummy variables.
The model is estimated using a Bayesian approach to allow for automatic selection of the changepoints and other model characteristics.
library(prophet)
The input to Prophet is always a dataframe with two columns: ds and y . The ds (datestamp) column should be of a format, ideally YYYY-MM-DD for a date or YYYY-MM-DD HH:MM:SS for a timestamp. The y column must be numeric, and represents the measurement we wish to forecast.
# sales montly
ggplot(df_merged_m, aes(x=month, y=sales_m)) +
geom_line() + ggtitle("Monthly Sales of Restaurant")
head(df_merged_m)
#Prophet model
# model with no seasonality
df_prophet_m <- df_merged_m[1:2]
head(df_prophet_m)
colnames(df_prophet_m) = c("ds", "y")
df_prophet_m$y <- exp(df_prophet_m$y)
prophet_sales_m <- prophet(df_prophet_m)
Disabling weekly seasonality. Run prophet with weekly.seasonality=TRUE to override this.
Disabling daily seasonality. Run prophet with daily.seasonality=TRUE to override this.
head(df_prophet_m)
# Step 2: Create a future dataframe for the next 14 months
future_sales_m <- make_future_dataframe(
prophet_sales_m,
periods = 14, # Forecast for 14 months
freq = 'month', # Monthly frequency
include_history = TRUE # Include historical data in the future dataframe
)
tail(future_sales_m)
forecast_sales_m <- predict(prophet_sales_m, future_sales_m)
tail(forecast_sales_m[c('ds', 'yhat', 'yhat_lower', 'yhat_upper')])
plot(prophet_sales_m, forecast_sales_m)
prophet_plot_components(prophet_sales_m, forecast_sales_m)
dyplot.prophet(prophet_sales_m, forecast_sales_m)
#Use the original dataframe to get the fitted values
fitted_values <- predict(prophet_sales_m, df_prophet_m)
# Extract the fitted values (column 'yhat' contains the fitted values)
fitted_y <- fitted_values$yhat
# Calculate RMSE
actual_y <- df_prophet_m$y # Actual sales values
rmse_prophet_m <- calculate_rmse(observed = actual_y, predicted = fitted_y)
# Print RMSE
cat("RMSE for Prophet Fitted Values:", rmse_prophet_m, "\n")
RMSE for Prophet Fitted Values: 16786939
Residuals for prophet
# Calculate Residuals
residuals_prophet <- actual_y - fitted_y # Residuals = Actual - Fitted
# Visualize Residuals using tsdisplay
tsdisplay(residuals_prophet, main = "Residual Diagnostics for Prophet Model")
# Perform ADF Test for Stationarity
adf_test <- adf.test(residuals_prophet)
cat("ADF Test p-value:", adf_test$p.value, "\n")
ADF Test p-value: 0.3278912
if (adf_test$p.value < 0.05) {
cat("Residuals are stationary (reject H0).\n")
} else {
cat("Residuals are not stationary (fail to reject H0).\n")
}
Residuals are not stationary (fail to reject H0).
# Perform Serial Correlation Test
ljung_box_test <- Box.test(residuals_prophet, lag = 10, type = "Ljung-Box")
cat("Ljung-Box Test p-value:", ljung_box_test$p.value, "\n")
Ljung-Box Test p-value: 6.527107e-10
if (ljung_box_test$p.value > 0.05) {
cat("Residuals resemble white noise (no significant autocorrelation).\n")
} else {
cat("Residuals show significant autocorrelation.\n")
}
Residuals show significant autocorrelation.
ggplot(df_merged_w, aes(x=week, y=sales_w)) +
geom_line() + ggtitle("Weekly Sales of Restaurant")
head(df_merged_w)
#Prophet model
# model with no seasonality
df_prophet_w <- df_merged_w[1:2]
colnames(df_prophet_w) = c("ds", "y")
df_prophet_w$y <- exp(df_prophet_w$y)
df_prophet_w
prophet_sales_w <- prophet(df_prophet_w)
Disabling weekly seasonality. Run prophet with weekly.seasonality=TRUE to override this.
Disabling daily seasonality. Run prophet with daily.seasonality=TRUE to override this.
Predictions are made on a dataframe with a column ds
containing the dates for which predictions are to be made. The
make_future_dataframe function takes the model object and a
number of periods to forecast and produces a suitable dataframe. By
default it will also include the historical dates so we can evaluate
in-sample fit.
future_sales_w <- make_future_dataframe(prophet_sales_w,
periods = 52,
freq = 'week',
include_history = T)
tail(future_sales_w)
As with most modeling procedures in R, we use the generic
predict function to get our forecast. The
forecast object is a dataframe with a column
yhat containing the forecast. It has additional columns for
uncertainty intervals and seasonal components.
# R
forecast_sales_w <- predict(prophet_sales_w, future_sales_w)
tail(forecast_sales_w[c('ds', 'yhat', 'yhat_lower', 'yhat_upper')])
plot(prophet_sales_w, forecast_sales_w)
You can use the prophet_plot_components function to see
the forecast broken down into trend, weekly seasonality, and yearly
seasonality.
prophet_plot_components(prophet_sales_w, forecast_sales_w)
dyplot.prophet(prophet_sales_w, forecast_sales_w)
# Use the original dataset to get fitted values
fitted_values_w <- predict(prophet_sales_w, df_prophet_w)
# Extract the fitted values (column 'yhat' contains the fitted values)
fitted_y_w <- fitted_values_w$yhat
# Ensure alignment between actual values (y) and fitted values (yhat)
actual_y_w <- df_prophet_w$y # Actual weekly sales values
# Calculate RMSE for weekly data
rmse_prophet_w <- calculate_rmse(observed = actual_y_w, predicted = fitted_y_w)
# Print RMSE
cat("RMSE for Prophet Fitted Values (Weekly):", rmse_prophet_w, "\n")
RMSE for Prophet Fitted Values (Weekly): 3319446
# Calculate Residuals
residuals_prophet_w <- actual_y_w - fitted_y_w # Residuals = Actual - Fitted
# Visualize Residuals using tsdisplay
tsdisplay(residuals_prophet_w, main = "Residual Diagnostics for Weekly Prophet Model")
# Perform ADF Test for Stationarity
adf_test_w <- adf.test(residuals_prophet_w)
cat("ADF Test p-value:", adf_test_w$p.value, "\n")
ADF Test p-value: 0.04400527
if (adf_test_w$p.value < 0.05) {
cat("Residuals are stationary (reject H0).\n")
} else {
cat("Residuals are not stationary (fail to reject H0).\n")
}
Residuals are stationary (reject H0).
# Perform Serial Correlation Test
ljung_box_test_w <- Box.test(residuals_prophet_w, lag = 10, type = "Ljung-Box")
cat("Ljung-Box Test p-value:", ljung_box_test_w$p.value, "\n")
Ljung-Box Test p-value: 7.638334e-14
if (ljung_box_test_w$p.value > 0.05) {
cat("Residuals resemble white noise (no significant autocorrelation).\n")
} else {
cat("Residuals show significant autocorrelation.\n")
}
Residuals show significant autocorrelation.
head(sales_d_ts)
Time Series:
Start = c(2021, 335)
End = c(2021, 340)
Frequency = 365
[1] 673701 1205301 1340901 1343701 360901 318801
plot(sales_d_ts)
sales_d_values <- as.numeric(sales_d_ts) # Extract numeric values
df_prophet_d <- data.frame(
ds = df_merged_d$date, # Dates
y = sales_d_values # Sales values
)
#Prophet model
#prophet_sales_d <- prophet(df_prophet, weekly.seasonality = TRUE)
prophet_sales_d <- prophet(df_prophet_d)
Disabling daily seasonality. Run prophet with daily.seasonality=TRUE to override this.
future_sales_d <- make_future_dataframe(prophet_sales_d,
periods = 60,
freq = 'day',
include_history = T)
tail(future_sales_d)
forecast_sales_d <- predict(prophet_sales_d, future_sales_d)
tail(forecast_sales_d[c('ds', 'yhat', 'yhat_lower', 'yhat_upper')])
plot(prophet_sales_d, forecast_sales_d)
prophet_plot_components(prophet_sales_d, forecast_sales_d)
dyplot.prophet(prophet_sales_d, forecast_sales_d)
# Extract fitted values for RMSE calculation
fitted_values_d <- predict(prophet_sales_d, df_prophet_d)
# Extract fitted values (column 'yhat')
fitted_y_d <- fitted_values_d$yhat
actual_y_d <- df_prophet_d$y # Actual sales values
# Step 8: Calculate RMSE
rmse_prophet_d <- calculate_rmse(observed = actual_y_d, predicted = fitted_y_d)
# Print RMSE
cat("RMSE for Prophet Fitted Values (Daily):", rmse_prophet_d, "\n")
RMSE for Prophet Fitted Values (Daily): 1022726
# Calculate Residuals
residuals_prophet_d <- actual_y_d - fitted_y_d # Residuals = Actual - Fitted
# Visualize Residuals using tsdisplay
tsdisplay(residuals_prophet_d, main = "Residual Diagnostics for Daily Prophet Model")
# Perform ADF Test for Stationarity
adf_test_d <- adf.test(residuals_prophet_d)
Warning: p-value smaller than printed p-value
cat("ADF Test p-value:", adf_test_d$p.value, "\n")
ADF Test p-value: 0.01
if (adf_test_d$p.value < 0.05) {
cat("Residuals are stationary (reject H0).\n")
} else {
cat("Residuals are not stationary (fail to reject H0).\n")
}
Residuals are stationary (reject H0).
# Perform Serial Correlation Test
ljung_box_test_d <- Box.test(residuals_prophet_d, lag = 20, type = "Ljung-Box")
cat("Ljung-Box Test p-value:", ljung_box_test_d$p.value, "\n")
Ljung-Box Test p-value: 0
if (ljung_box_test_d$p.value > 0.05) {
cat("Residuals resemble white noise (no significant autocorrelation).\n")
} else {
cat("Residuals show significant autocorrelation.\n")
}
Residuals show significant autocorrelation.
rmse_list <- c(rmse_ols_m, rmse_ols_w, rmse_ols_d,
rmse_bm_m, rmse_bm_w, rmse_bm_d,
rmse_ggm1, rmse_ggm_w, rmse_ggm_d,
rmse_hw2,
rmse_auto_arima, rmse_auto_arima_w, rmse_auto_arima_d,
rmse_sarima_d,
rmse_sarimax_d,
rmse_exp_sm_m, rmse_exp_sm_w, rmse_exp_sm_m,
rmse_mixture_m, rmse_mixture_w, rmse_mixture_d,
rmse_prophet_m, rmse_prophet_w, rmse_prophet_d
)
rmse_list
[1] 13229295 3909103 1425907 18498870 4542019 1651896
[7] 11759505 3488834 1600828 13169921 15118942 3339058
[13] 1094980 1094980 1146332 16189623 3340420 16189623
[19] 6978426 1202671 1182471 16786939 3319446 1022726
# Initialize an empty data frame for RMSE values
rmse_table <- data.frame(
Model = character(),
Monthly = numeric(),
Weekly = numeric(),
Daily = numeric(),
stringsAsFactors = FALSE
)
# Monthly RMSE values
rmse_monthly <- c(
"OLS" = rmse_ols_m,
"Bass_Model" = rmse_bm_m,
"GGM" = rmse_ggm1,
"Holt_Winters" = rmse_hw2,
"Arima" = rmse_auto_arima,
"Exp_Smooth" = rmse_exp_sm_m,
"GGM+SARIMA" = rmse_mixture_m,
"Prophet" = rmse_prophet_m
)
# Weekly RMSE values
rmse_weekly <- c(
"OLS" = rmse_ols_w,
"Bass_Model" = rmse_bm_w,
"GGM" = rmse_ggm_w,
"Holt_Winters" = NaN,
"Arima" = rmse_auto_arima_w,
"Exp_Smooth" = rmse_exp_sm_w,
"GGM+SARIMA" = rmse_mixture_w,
"Prophet" = rmse_prophet_w
)
# Daily RMSE values
rmse_daily <- c(
"OLS" = rmse_ols_d,
"Bass_Model" = rmse_bm_d,
"GGM" = rmse_ggm_d,
"Holt_Winters" = NaN,
"Arima" = rmse_auto_arima_d,
"Exp_Smooth" = rmse_exp_sm_d,
"GGM+SARIMA" = rmse_mixture_d,
"Prophet" = rmse_prophet_d
)
# Combine RMSE values into a table
for (model_name in names(rmse_monthly)) {
rmse_table <- rbind(rmse_table, data.frame(
Model = model_name,
Monthly = rmse_monthly[model_name],
Weekly = rmse_weekly[model_name],
Daily = rmse_daily[model_name]
))
}
# View the RMSE table
print(rmse_table)
NA
Best models are:
# target variable
test_sales_df <- read_excel("data/sales/test_data.xlsx")
head(test_sales_df)
df_sales_m_test <- test_sales_df %>%
mutate(month = floor_date(date, "month")) %>% # Extract month
group_by(month) %>%
summarise(sales_m = sum(sales_cop), bar_m = sum(bar), food_m = sum(food)
) # Summing values
head(df_sales_m_test)
## sales weekly
df_sales_w_test <- test_sales_df %>%
mutate(week = floor_date(date, "week")) %>% # Extract month
group_by(week) %>%
summarise(sales_w = sum(sales_cop), bar_w = sum(bar), food_w = sum(food)) # Summing values
head(df_sales_w_test)
cumsum(sales_m_ts)
[1] 7925601 33539060 65492343 107418523 144885201
[6] 202811448 282434292 371250728 476444489 569781277
[11] 660649764 762658574 854895801 951384432 1061951572
[16] 1169736471 1296038865 1408776880 1527683850 1642578141
[21] 1761369195 1864564540 1963627555 2050162367 2171930992
[26] 2303345161 2427895903 2547368818 2682080320 2778534518
[31] 2893079374 3002614398 3139212388 3265637545 3369541574
[36] 3515788921
forecast_cumulative
Time Series:
Start = 37
End = 38
Frequency = 1
[37,] [38,]
8217316481 1585965110